{"id":12876,"date":"2014-02-04T18:46:00","date_gmt":"2014-02-04T18:46:00","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=12876"},"modified":"2026-03-28T11:34:12","modified_gmt":"2026-03-28T16:34:12","slug":"angles","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/angles\/","title":{"rendered":"Angles"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_KCHfDppcnJA\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_KCHfDppcnJA\" data-source-videoID=\"KCHfDppcnJA\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Angles Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Angles\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_KCHfDppcnJA:hover {cursor:pointer;} img#videoThumbnailImage_KCHfDppcnJA {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/1231-angles-2-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_KCHfDppcnJA\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_KCHfDppcnJA\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Angles\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_KCHfDppcnJA\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_KCHfDppcnJA\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_KCHfDppcnJA\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction cZK_Function() {\n  var x = document.getElementById(\"cZK\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"cZK_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"cZK\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_a_Ray\" class=\"smooth-scroll\">What is a Ray?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#What_is_a_Vertex\" class=\"smooth-scroll\">What is a Vertex?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Labeling_Angles\" class=\"smooth-scroll\">Labeling Angles<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Measuring_Angles\" class=\"smooth-scroll\">Measuring Angles<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_Problems\" class=\"smooth-scroll\">Example Problems<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Review\" class=\"smooth-scroll\">Review<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Frequently_Asked_Questions\" class=\"smooth-scroll\">Frequently Asked Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Angle_Practice_Questions\" class=\"smooth-scroll\">Angle Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"FAQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"FAQs\">FAQs<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video about angles.<\/p>\n<h2><span id=\"What_is_a_Ray\" class=\"m-toc-anchor\"><\/span>What is a Ray?<\/h2>\n<p>\nLet\u2019s start by defining a ray. A ray is a line with a single endpoint that extends infinitely in one direction.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/ray-2.png\" alt=\"\" width=\"557.9\" height=\"111.3\" class=\"aligncenter size-full wp-image-88600\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/ray-2.png 1594w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/ray-2-300x60.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/ray-2-1024x204.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/ray-2-768x153.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/ray-2-1536x306.png 1536w\" sizes=\"(max-width: 1594px) 100vw, 1594px\" \/><\/p>\n<p>If we take this ray and add another ray to it that has the same endpoint, we\u2019ve created an <strong>angle<\/strong>.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/angle-3.png\" alt=\"\" width=\"454.8\" height=\"340\" class=\"aligncenter size-full wp-image-88597\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/angle-3.png 1137w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/angle-3-300x224.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/angle-3-1024x766.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/angle-3-768x574.png 768w\" sizes=\"(max-width: 1137px) 100vw, 1137px\" \/><\/p>\n<h2><span id=\"What_is_a_Vertex\" class=\"m-toc-anchor\"><\/span>What is a Vertex?<\/h2>\n<p>\nWe\u2019ve also created a vertex, which is the point where the two rays meet. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/vertex.png\" alt=\"\" width=\"453.6\" height=\"305.55\" class=\"aligncenter size-full wp-image-88603\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/vertex.png 1296w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/vertex-300x202.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/vertex-1024x690.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/vertex-768x517.png 768w\" sizes=\"(max-width: 1296px) 100vw, 1296px\" \/><\/p>\n<p>You can think of it as a corner. We usually see vertices whenever lines meet or in <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/polygons\/\">polygons<\/a> like <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/area-and-perimeter-of-a-triangle\/\">triangles<\/a> and quadrilaterals. <\/p>\n<h2><span id=\"Labeling_Angles\" class=\"m-toc-anchor\"><\/span>Labeling Angles<\/h2>\n<p>\nSometimes we have many angles, so in order to tell them apart, we have a system for naming them. Here\u2019s our simple angle again but with a few points added on the rays: <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-and-c.png\" alt=\"\" width=\"429.1\" height=\"327.6\" class=\"aligncenter size-full wp-image-88759\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-and-c.png 1226w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-and-c-300x229.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-and-c-1024x782.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-and-c-768x586.png 768w\" sizes=\"(max-width: 1226px) 100vw, 1226px\" \/><\/p>\n<p>Now we can refer to our angle as angle ABC (\u2220ABC). When naming angles with three letters, the vertex point must be in the middle. Here, B is the vertex so the B goes between the A and the C. We can actually call this \u2220CBA and it is just as correct. <\/p>\n<p>If the point that is the vertex is only a part of one angle then we can use a shorter name. In this case, we could also call this angle B. Be careful though, because sometimes a single point can be the vertex of multiple angles, like this:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-c-d.png\" alt=\"\" width=\"359.45\" height=\"327.6\" class=\"aligncenter size-full wp-image-88798\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-c-d.png 1072w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-c-d-300x262.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-c-d-1024x894.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-c-d-768x671.png 768w\" sizes=\"(max-width: 1072px) 100vw, 1072px\" \/><\/p>\n<p>In this case, we\u2019d have to call the angles by their long names, because point B is the vertex of \u2220ABC, \u2220DBC, and \u2220DBA! If we asked someone to just look at \u2220B they wouldn\u2019t know which of these we meant. So it\u2019s important to be precise when dealing with more than one angle.<\/p>\n<p>Sometimes angles will be labeled with numbers inside the arc, like this:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-c-1.png\" alt=\"\" width=\"448.8\" height=\"320.8\" class=\"aligncenter size-full wp-image-88813\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-c-1.png 1122w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-c-1-300x214.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-c-1-1024x732.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/a-b-c-1-768x549.png 768w\" sizes=\"(max-width: 1122px) 100vw, 1122px\" \/><\/p>\n<p>Now we have an additional name for this angle. We can now call it \u22201 or we can call it \u2220ABC or we can call it \u2220B. Since most of us have three names, it\u2019s only fair that angles have a bunch too. But most of the time we like to use letters to name our angles, since the numbers could be confused with the measure of an angle. Sometimes you\u2019ll see lowercase letters instead of numbers or Greek symbols like \\(\\theta\\) or \\(\\alpha\\). <\/p>\n<h2><span id=\"Measuring_Angles\" class=\"m-toc-anchor\"><\/span>Measuring Angles<\/h2>\n<p>\nSpeaking of measuring, remember the protractor? We use it to measure angles. If we were to place one on our trusty angle we would find that it measures 45 degrees:<\/p>\n<p>If we wrote this out, we would write it like this:<\/p>\n<div class=\"examplesentence\">\\(m\u2220ABC = 45\u00b0\\)<\/center><\/div>\n<p>\n&nbsp;<br \/>\nThe measure of an angle is important in classifying angles, as we\u2019re about to see. <\/p>\n<p>Let\u2019s look at a variation of our two-ray angle, but this time let\u2019s make it so that they are <strong>perpendicular<\/strong> to each other, which means the angle between them is 90 degrees:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/90-degrees.png\" alt=\"\" width=\"322\" height=\"307.3\" class=\"aligncenter size-full wp-image-88915\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/90-degrees.png 920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/90-degrees-300x286.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/90-degrees-768x733.png 768w\" sizes=\"(max-width: 920px) 100vw, 920px\" \/><\/p>\n<p>Here, we\u2019ve created a <strong>right angle<\/strong>. Notice that it has a different angle symbol than our first angle. Instead of an arc, it has a square. Whenever we see an angle with that square we know it is exactly 90 degrees. We most often see right angles in <strong>squares<\/strong>, <strong>rectangles<\/strong>, and <strong>right triangles<\/strong>, but they can appear in other places too.<\/p>\n<p>When an angle has a measure that is smaller than 90 degrees, it\u2019s called an <strong>acute triangle<\/strong>. Our original angle would be part of an acute triangle, since it measures 45 degrees, which is less than 90:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/45-degrees.png\" alt=\"\" width=\"482.4\" height=\"362.7\" class=\"aligncenter size-full wp-image-88918\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/45-degrees.png 1072w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/45-degrees-300x226.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/45-degrees-1024x770.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/45-degrees-768x577.png 768w\" sizes=\"(max-width: 1072px) 100vw, 1072px\" \/><\/p>\n<p>If we make an angle so that it has a measure that is greater than 90 degrees, we create an <strong>obtuse angle<\/strong>, which looks like this:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/140-degrees.png\" alt=\"\" width=\"518.4\" height=\"255\" class=\"aligncenter size-full wp-image-88921\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/140-degrees.png 1728w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/140-degrees-300x148.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/140-degrees-1024x504.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/140-degrees-768x378.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/140-degrees-1536x756.png 1536w\" sizes=\"(max-width: 1728px) 100vw, 1728px\" \/><\/p>\n<p>In this case, angle ABC has a measure of 140 degrees, which is greater than 90. Obtuse angles also have to be less than 180 degrees.<\/p>\n<p>Those are the three main types of angles as determined by measure, but there are two more oddballs we need to know about.<\/p>\n<p>The first is a <strong>straight angle<\/strong>. It looks like a straight line, and it has a measure of 180 degrees.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/straight-angle.png\" alt=\"\" width=\"566.4\" height=\"196.8\" class=\"aligncenter size-full wp-image-88927\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/straight-angle.png 1888w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/straight-angle-300x104.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/straight-angle-1024x356.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/straight-angle-768x267.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/straight-angle-1536x534.png 1536w\" sizes=\"(max-width: 1888px) 100vw, 1888px\" \/><\/p>\n<p>When it\u2019s drawn like this, we can see that \u2220ABC does exist and has a measure of 180 degrees. This is a useful thing to know because we\u2019ll need it to understand linear pairs later on. <\/p>\n<p>But before we get to that, let\u2019s look at the other oddball. This one doesn\u2019t look like an angle at all:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/full-angle-2.png\" alt=\"\" width=\"452.8\" height=\"129.6\" class=\"aligncenter size-full wp-image-88948\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/full-angle-2.png 1132w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/full-angle-2-300x86.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/full-angle-2-1024x293.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/full-angle-2-768x220.png 768w\" sizes=\"(max-width: 1132px) 100vw, 1132px\" \/><\/p>\n<p>But in fact, it\u2019s called a <strong>full angle<\/strong>. Imagine we rotated point A counterclockwise, with point B staying where it is, until it lined up with point C again. How many degrees is that? It\u2019s all the way around the circle, which we know is 360\u00b0.<\/p>\n<p>Remember our straight angle? What if we drew that but added another ray sticking out of it, like this:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/angles.png\" alt=\"\" width=\"573\" height=\"278.4\" class=\"aligncenter size-full wp-image-88945\" style=\"box-shadow: 3px 3px 10px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/angles.png 1910w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/angles-300x146.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/angles-1024x498.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/angles-768x373.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/angles-1536x746.png 1536w\" sizes=\"(max-width: 1910px) 100vw, 1910px\" \/><\/p>\n<p>If we know that angle DBC is 55 degrees, and we know that angle ABC is a straight angle and therefore 180 degrees, we can actually find angle ABD! How? By taking the whole straight angle (\u2220ABC) that measures 180 degrees and subtracting the smaller angle (\u2220DBC) that measures 55 degrees. \\(180\u00b0 \u2013 55\u00b0 = 125\u00b0\\). This is called a <strong>linear pair<\/strong>. <\/p>\n<p>Two angles (\u2220ABD &#038; \u2220DBC) combine to form \u2220ABC, which is a line. And because the two smaller angles add up to 180 degrees, we can also say that they are <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/supplementary-angles\/\">supplementary angles<\/a>.<\/p>\n<p>Something very similar happens with right angles. Here\u2019s our right angle from before, but with another ray in the middle:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/right-angle-rayu.png\" alt=\"\" width=\"351.6\" height=\"327.6\" class=\"aligncenter size-full wp-image-88951\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/right-angle-rayu.png 1172w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/right-angle-rayu-300x280.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/right-angle-rayu-1024x954.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/right-angle-rayu-768x716.png 768w\" sizes=\"(max-width: 1172px) 100vw, 1172px\" \/><\/p>\n<p>Angle DEF is a right angle. We can see that \u2220DEG and \u2220GEF together completely fill \u2220DEF, which means they add up to 90 degrees. So if we know one of the two angles we can find the other one by subtracting its measure from 90 degrees. For instance, if \u2220DEG is 30\u00b0 then we know that \u2220GEF is 60\u00b0 because 90\u00b0 \u2013 30\u00b0 = 60\u00b0. Angles that add up to 90\u00b0 are called <strong>complementary angles<\/strong>. <\/p>\n<p>Let\u2019s go back to our obtuse angle one more time. There\u2019s one more type of angle that\u2019s been hiding in plain sight that we need to be aware of.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/reflexc-part-1.png\" alt=\"\" width=\"474\" height=\"228\" class=\"aligncenter size-full wp-image-88957\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/reflexc-part-1.png 1580w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/reflexc-part-1-300x144.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/reflexc-part-1-1024x493.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/reflexc-part-1-768x369.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/reflexc-part-1-1536x739.png 1536w\" sizes=\"auto, (max-width: 474px) 100vw, 474px\" \/><\/p>\n<p>We can see that \u2220ABC is an obtuse angle, which means it\u2019s more than 90\u00b0 and less than 180\u00b0. But what about the other side?<\/p>\n<p>This is called a <strong>reflex angle<\/strong>. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/reflex-part-2.png\" alt=\"\" width=\"454.5\" height=\"234.6\" class=\"aligncenter size-full wp-image-88954\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/reflex-part-2.png 1515w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/reflex-part-2-300x155.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/reflex-part-2-1024x529.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/reflex-part-2-768x396.png 768w\" sizes=\"(max-width: 1515px) 100vw, 1515px\" \/><\/p>\n<p>It\u2019s always more than 180\u00b0 and less than 360\u00b0. Every acute, right, and obtuse angle has a reflex angle.<\/p>\n<h2><span id=\"Example_Problems\" class=\"m-toc-anchor\"><\/span>Example Problems<\/h2>\n<p>\nNext, let\u2019s take a look at where we\u2019ll see some of these angles in the wild, or at least in geometry problems. <\/p>\n<p>Let\u2019s start by looking at two lines that intersect. In this case, we\u2019ve numbered the angles.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one.png\" alt=\"\" width=\"493.5\" height=\"260.4\" class=\"aligncenter size-full wp-image-88960\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one.png 1645w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one-300x158.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one-1024x540.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one-768x405.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one-1536x810.png 1536w\" sizes=\"(max-width: 1645px) 100vw, 1645px\" \/><\/p>\n<p>Whenever we see a figure like this, if we know any of the angles we can determine all of the others! So if \u22201 measures 130\u00b0, we can figure out \u22202 because those two angles together form a line and are a linear pair and supplementary. So \u22202 must be 50\u00b0. The same works for angles 1 and 3. And then we can use what we know about \u22202 to pair it up with \u22204 to find that angle. When it\u2019s all said and done it looks like this:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one-part-2.png\" alt=\"\" width=\"475.2\" height=\"244.8\" class=\"aligncenter size-full wp-image-88969\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one-part-2.png 1584w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one-part-2-300x155.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one-part-2-1024x528.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one-part-2-768x396.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/example-one-part-2-1536x791.png 1536w\" sizes=\"(max-width: 1584px) 100vw, 1584px\" \/><\/p>\n<p>Notice that the angles opposite one another have the same measure. These angles are called <strong>vertical angles<\/strong>, and they\u2019re always <a href=\"https:\/\/www.mometrix.com\/academy\/congruent-angles\/\"><strong>congruent<\/strong><\/a>, which is geometry-speak for having the same measure.<\/p>\n<p>Now let\u2019s look at three lines intersecting:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-one.png\" alt=\"\" width=\"550.8\" height=\"268.5\" class=\"aligncenter size-full wp-image-88972\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-one.png 1836w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-one-300x146.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-one-1024x499.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-one-768x374.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-one-1536x749.png 1536w\" sizes=\"(max-width: 1836px) 100vw, 1836px\" \/><\/p>\n<p>This is called a <strong>transversal<\/strong>. Once again we\u2019ve numbered the angles, and there are red arrow marks on two of the lines, indicating that they are parallel. A transversal doesn\u2019t have to have parallel lines but when it is, it allows us to know a lot about the eight angles created by the intersecting lines.<\/p>\n<p>But before we get to that, let\u2019s look at the eight angles. We can see they are in two groups of four (angles 1-4 and 5-8). Angle 1 is in the top-left position in the top group of angles. If we look at the same spot in the bottom group of angles we see that \u22205 is in the top-left spot for that group. That means that \u22201 and \u22205 are corresponding angles. So \u22202 and \u22206 are also corresponding angles because they\u2019re in the top right spot for their respective groups. \u22203 and \u22207 are also corresponding, as are \u22204 and \u22208. In a transversal, when there\u2019s a pair of parallel lines, corresponding angles are congruent. When the lines are not parallel, the corresponding angles are not congruent.<\/p>\n<p>In the case of our diagram that does have parallel lines, if we know that \u22202 is 55\u00b0 we then know that \u22206 is also 55\u00b0. And once we know that, we can use what we learned about vertical angles and linear pairs to find all the others:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-two.png\" alt=\"\" width=\"557.4\" height=\"274.2\" class=\"aligncenter size-full wp-image-88975\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-two.png 1858w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-two-300x148.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-two-1024x504.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-two-768x378.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/transversal-part-two-1536x756.png 1536w\" sizes=\"(max-width: 1858px) 100vw, 1858px\" \/><\/p>\n<p>That\u2019s all we need to know to find our angles, but there is some more location-based vocabulary we need to be aware of with these types of problems. <strong>Interior angles<\/strong> are the angles between the parallel lines. In this case, that\u2019s \u22203, \u22204, \u22205, and \u22206. The exterior angles are the ones that, you guessed it, are not between the parallel lines. So \u22201, \u22202, \u22207, and \u22208 are exterior angles.<\/p>\n<p><strong>Alternate<\/strong> angles are angles that are on opposite sides of the line that cuts across the parallel lines. And same-side angles are angles that are on the same side of that line, of course. <\/p>\n<p>In questions about the two groups of angles, this is used to combine interior or exterior with alternate or same side angles. The question will always relate to the other group of angles. Something like \u201cwhat is the alternate interior angle for \u22203?\u201d We would look to the other group of angles, then to the other side of the intersecting line, and then find the only angle that is an interior angle, which would be \u22206. The same side interior angle for \u22203 is \u22205.<\/p>\n<hr>\n<h2><span id=\"Review\" class=\"m-toc-anchor\"><\/span>Review<\/h2>\n<p>\nThat\u2019s a lot to absorb in a small amount of time. Referencing the image above, try these questions to see if it has sunk in: <\/p>\n<p>1. What is the alternate exterior angle to \u22208? <\/p>\n<div style=\"text-align: center; margin-bottom: 20px;\"><button class=\"buttontranscript\" onClick=\"toggle('Answer1')\">Show Answer<\/button><\/div>\n<div id=\"Answer1\" style=\"display:none; box-shadow: 1.5px 1.5px 5px grey; background-color:#E0E0E0; padding: 30px; padding-bottom: 15px; width: 60%; margin: auto; text-align: center;\">\nThe alternate exterior angle to \u22208 is \u22201.<\/p>\n<p style=\"text-align: left;\">\n<\/div>\n<p>\n&nbsp;<br \/>\n2. What is the same side exterior angle to \u22207?<\/p>\n<div style=\"text-align: center; margin-bottom: 20px;\"><button class=\"buttontranscript\" onClick=\"toggle('Answer2')\">Show Answer<\/button><\/div>\n<div id=\"Answer2\" style=\"display:none; box-shadow: 1.5px 1.5px 5px grey; background-color:#E0E0E0; padding: 30px; padding-bottom: 15px; width: 60%; margin: auto; text-align: center;\">\nThe same side exterior angle to \u22207 is \u22201.<\/p>\n<p style=\"text-align: left;\">\n<\/div>\n<p>\n&nbsp;<br \/>\n3. What is the corresponding angle to \u22205?<\/p>\n<div style=\"text-align: center; margin-bottom: 20px;\"><button class=\"buttontranscript\" onClick=\"toggle('Answer3')\">Show Answer<\/button><\/div>\n<div id=\"Answer3\" style=\"display:none; box-shadow: 1.5px 1.5px 5px grey; background-color:#E0E0E0; padding: 30px; padding-bottom: 15px; width: 60%; margin: auto; text-align: center;\">\nThe corresponding angle to \u22205 is \u22201.<\/p>\n<p style=\"text-align: left;\">\n<\/div>\n<p>\n&nbsp;<br \/>\nThanks for watching, and happy angling!<\/p>\n<ul class=\"citelist\">\n<li><a href=\"https:\/\/www.mathopenref.com\/angle.html\"target=\"_blank\">\u201cAngle &#8211; Math Word Definition &#8211; Math Open Reference.\u201d n.d.<\/a><\/li>\n<\/ul>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Frequently_Asked_Questions\" class=\"m-toc-anchor\"><\/span>Frequently Asked Questions<\/h2>\n<div class=\"faq-list\">\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What are complementary angles?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Complementary angles are two angles whose measures add up to 90 degrees.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is a supplementary angle?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>A supplementary angle is an angle that adds to another angle to equal 180\u00b0. For example, the angle supplementary to a 107\u00b0 angle would be \\(180 &#8211; 107 = 73\u00b0\\).<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What are vertical angles?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Vertical angles are pairs of angles opposite one another. One vertical angle always equals the other vertical angle.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Vertical-angles-example.svg\" alt=\"Two intersecting straight lines form angles at point B, with two opposite angles labeled as 27 degrees each. Points A, B, C, D, and E are marked on the lines.\" width=\"356\" height=\"149\" class=\"aligncenter size-full wp-image-273955\"  role=\"img\" \/><\/p>\n<p>Here, \u2220ABC and \u2220DBE are vertical angles.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What are corresponding angles?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Corresponding angles are angles that are in the same position relative to the transversal and a parallel line when two lines are cut by a transversal. Corresponding angles always have the same measure.<\/p>\n<p> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Corresponding-angles-example.svg\" alt=\"Two parallel lines are intersected by a diagonal line, forming two labeled angles, 1 and 2, at the points of intersection.\" width=\"290\" height=\"140\" class=\"aligncenter size-full wp-image-273958\"  role=\"img\" \/><\/p>\n<p>Here, \u22201 and \u22202 are corresponding angles.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is an acute angle?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>An acute angle is an angle whose measure is less than 90 degrees.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the angle of a triangle?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Find the angle of a right triangle by using these three formulas: <\/p>\n<p style=\"text-align: center; line-height: 65px\">\\(\\sin\u2061 \\theta =\\dfrac{\\text{opposite}}{\\text{hypotenuse}}\\)<br \/>\\(\\cos \\theta =\\dfrac{\\text{adjacent}}{\\text{hypotenuse}}\\)<br \/>\\(\\tan \u2061\\theta =\\dfrac{\\text{opposite}}{\\text{adjacent}}\\)<\/p>\n<p>These formulas can be remembered using the mnemonic SOH-CAH-TOA. Fill in the given side lengths and work backwards to solve for the angle (\\(\\theta\\) ).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Finding-angle-of-triangle-example.svg\" alt=\"Diagram of a right triangle labeled with sides: adjacent, opposite, hypotenuse; and angle \u03b8 near the adjacent and hypotenuse sides.\" width=\"222\" height=\"241\" class=\"aligncenter size-full wp-image-273964\"  role=\"img\" \/><\/p>\n<div class=\"lightbulb-example-2\" style=\"min-width: 70%\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Find the value of \\(\\theta\\).<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Finding-angle-of-triangle-example-2.svg\" alt=\"Right triangle with a base of 4 units, hypotenuse of 5 units, and an angle \u03b8 opposite the perpendicular side.\" width=\"304\" height=\"241\" class=\"aligncenter size-full wp-image-273961\"  role=\"img\" \/><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">You are given the opposite and hypotenuse, so use the following formula:<\/p>\n<p style=\"text-align: center\">\\(\\sin \u2061\\theta =\\dfrac{\\text{opposite}}{\\text{hypotenuse}}\\)<\/p>\n<p>Fill in your given values.<\/p>\n<p style=\"text-align: center\">\\(\\sin \\theta =\\dfrac{4}{5}\\)<\/p>\n<p>Then, work backwards to solve for \\(\\theta\\).<\/p>\n<p style=\"text-align: center; margin-bottom: 0em; line-height: 45px\">\\(\\theta =\\sin ^{-1}\\frac{4}{5}\\)<br \/>\\(\\theta \\approx 53.13\u00b0\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is an obtuse angle?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>An obtuse angle is any angle that measures greater than 90\u00b0.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Obtuse-angle-example.svg\" alt=\"Two straight lines form an obtuse angle measuring 127 degrees, with the angle clearly labeled.\" width=\"298\" height=\"153\" class=\"aligncenter size-full wp-image-273967\"  role=\"img\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Angle_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Angle Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for \\(x\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Solve-for-x.svg\" alt=\"A right angle split into two angles: one labeled 37\u00b0, the other labeled x. The angles are formed by three arrows meeting at a common point.\" width=\"206\" height=\"189\" class=\"aligncenter size-full wp-image-274126\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">43\u00b0<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">53\u00b0<\/div><div class=\"PQ\"  id=\"PQ-1-3\">137\u00b0 <\/div><div class=\"PQ\"  id=\"PQ-1-4\">90\u00b0<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The sum of \\(x\\) and 37\u00b0 will be 90\u00b0 because these two angles are complementary. Here, \\(x\\) can be calculated by subtracting 37 from 90. Either way, \\(x=53\u00b0\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich angle pair would be considered vertical angles? <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70934 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-parallel-lines-and-an-intersecting-line-with-8-angles.png\" alt=\"2 parallel lines and an intersecting line with 8 angles\" width=\"318\" height=\"213\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-parallel-lines-and-an-intersecting-line-with-8-angles.png 1044w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-parallel-lines-and-an-intersecting-line-with-8-angles-300x201.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-parallel-lines-and-an-intersecting-line-with-8-angles-1024x687.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-parallel-lines-and-an-intersecting-line-with-8-angles-768x515.png 768w\" sizes=\"auto, (max-width: 318px) 100vw, 318px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">Angle 6 and Angle 8 <\/div><div class=\"PQ\"  id=\"PQ-2-2\">Angle 3 and Angle 8 <\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-3\">Angle 5 and Angle 8 <\/div><div class=\"PQ\"  id=\"PQ-2-4\">Angle 1 and Angle 8 <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Vertical angles are also known as opposite angles. Opposite angles, or vertical angles, in the diagram include: 1 and 4, 2 and 3, 5 and 8, and 6 and 7.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich angle description matches the angle below?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Obtuse-angle-example.svg\" alt=\"Two straight lines form an obtuse angle measuring 127 degrees, with the angle clearly labeled.\" width=\"298\" height=\"153\" class=\"aligncenter size-full wp-image-273967\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">Right angle<\/div><div class=\"PQ\"  id=\"PQ-3-2\">Acute angle<\/div><div class=\"PQ\"  id=\"PQ-3-3\">Full angle<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">Obtuse angle<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nMax sets up a sprinkler so that it sprays a 90\u00b0 section of his lawn. He plans on rotating the sprinkler every 15 minutes so that the entire lawn receives water. How many times will the sprinkler need to be rotated so that the entire lawn is watered?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">Four times total<\/div><div class=\"PQ\"  id=\"PQ-4-2\">Five times total<\/div><div class=\"PQ\"  id=\"PQ-4-3\">Two times total<\/div><div class=\"PQ\"  id=\"PQ-4-4\">Six times total<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Each time the sprinkler is set up it waters one quarter of the entire lawn. This means that the sprinkler needs to be rotated four times in order to reach each section.<\/p>\n<p style=\"text-align: center\">\\(90\u00b0 \\times 4\\text{ sections}=360\u00b0\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nA walking path crosses over a set of train tracks creating a transversal line. If the measure of Angle 1 is 120 degrees, what is the measure of Angle 3?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70946 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-parallel-lines-with-an-intersecting-line.png\" alt=\"2 parallel lines with an intersecting line\" width=\"369\" height=\"254\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-parallel-lines-with-an-intersecting-line.png 1032w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-parallel-lines-with-an-intersecting-line-300x207.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-parallel-lines-with-an-intersecting-line-1024x705.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-parallel-lines-with-an-intersecting-line-768x529.png 768w\" sizes=\"auto, (max-width: 369px) 100vw, 369px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">120 degrees<\/div><div class=\"PQ\"  id=\"PQ-5-2\">70 degrees<\/div><div class=\"PQ\"  id=\"PQ-5-3\">50 degrees<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-4\">60 degrees<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Angles 1 and 3 are supplementary angles. The sum of Angles 1 and 3 will be 180 degrees. If Angle 1 is 120 degrees, then \\(180-120\\) gives us the value of Angle 3.<\/p>\n<p>Therefore, Angle 3 is 60 degrees.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/geometry\/\">Return to Geometry Videos<\/a><\/p>\n<\/div>\n<p><script>\nfunction toggle(obj) {\n          var obj=document.getElementById(obj);\n          if (obj.style.display == \"block\") obj.style.display = \"none\";\n          else obj.style.display = \"block\";\n}\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Return to Geometry Videos<\/p>\n","protected":false},"author":1,"featured_media":100324,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-12876","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-angle-videos","7":"page_category-math-advertising-group","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/12876","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=12876"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/12876\/revisions"}],"predecessor-version":[{"id":280976,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/12876\/revisions\/280976"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100324"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=12876"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}