# What is a Supplementary Angle?

Supplementary Angles

A pair of supplementary angles is two angles whose measures sum to 180º. An example of a pair of supplementary angles is a 110º angle and a 70º angle.

Let’s take a look at an example:

Here is a straight line, let’s call it Z, it is 180º. Another line, let’s call it Y, intersects Z and creates two angles. The one (b) is obviously bigger than 90º and is therefore obtuse. The other (a) is smaller than 90º and is therefore acute. These two angles are complementary, because they will always add up to 180º.

Let’s try our hand at a few practice problems. Here are two angles. One is 34 degrees, and we can see they are supplementary since they are on a straight line. So, if we know that supplementary angles add up to 180 degrees, we can simply subtract 34 from 180 to find the angle x. In this case, x = 146 degrees

One last one. Can you figure this one out by yourself? I’ll give you a few seconds. The answer is y = 12 degrees. Because 180 – 168 = 12. Make sense?

I hope that helps. Thanks for watching this video lesson. Until next time, happy studying.

## Practice Questions

Question #1:

What is the measure of an angle supplementary to an angle measuring 31°?

123°

149°

63°

59°

The correct answer is 149°. Supplementary angles are two angles that add to 180°. To find a supplementary angle, subtract the known angle from 180°.
$$180°-31°=149°$$
The angle supplementary to a 31° angle is a 149° angle.

Question #2:

What measure do supplementary angles add to?

90°

180°

270°

360°

The correct answer is 180°. Supplementary angles are two angles that add to 180°.

Question #3:

Choose the pair of supplementary angles.

42° and 63°

37° and 53°

18° and 121°

23° and 157°

The correct answer is 23° and 157°. Supplementary angles are two angles that add to 180°. Check each pair.
$$42°+63°=105°$$
$$37°+53°=90°$$
$$18°+121°=139°$$
$$23°+157°=180°$$

Question #4:

What is the measure of the angle supplementary to an angle measuring 129°?

104°

111°

51°

67°

The correct answer is 51°. Supplementary angles are two angles that add to 180°. To find a supplementary angle, subtract the known angle from 180°.
$$180°-129°=51°$$
The angle supplementary to a 129° angle is a 51° angle.

Question #5:

Choose the pair of supplementary angles.

67° and 113°

38° and 73°

67° and 23°

124° and 59°

$$67°+113°=180°$$
$$38°+73°=111°$$
$$67°+23°=90°$$
$$124°+59°=183°$$