What is a Complementary Angle?

Complementary Angles

Hi, welcome this video lesson on complementary angles. Now complementary angles are 2 angles that, when added together, equal 90 degrees. No, not that kind of 90 degrees. 90 degrees. Yes, that’s better. Now let’s take a look at a few examples to see how this works.

Here is an angle, let’s presume it’s 90 degrees. Another line intersects it and creates 2 angles, one b, one a. B is 60 degrees, a is 30 degrees. When added together we end up getting 90 degrees. This is a pair of complementary angles.

Let’s try our hand at a couple practice problems. Here are 2 angles. Assuming these are complementary, what angle is x? To find this out, we only need to do a bit of subtraction. We know that a complementary angle is 90 degrees, so if we subtract 34 from 90, we get 56. 56 degrees is equal to x, because that’s what must be added to 34 in order to get 90 and make the angle complementary.

One last one. Let’s see if you can figure this one out by yourself. The answer is x will always equal 46. Here’s why. If we know that this angle is complementary and we subtract 44 degrees from that we know that that leaves us with 46. Make sense? I hope that helps. Thanks so much for watching this video lesson, and until next time, happy studying!

Practice Questions

Question #1:

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

123°

149°

63°

59°

The correct answer is 59°. Complementary angles add to 90°, so to find a complementary angle, subtract the known angle from 90°.
$$90°-31°=59°$$
The angle complementary to a 31° angle is 59°.

Question #2:

What measure do two complementary angles add up to?

60°

90°

180°

360°

The correct answer is 90°. Complementary angles are two angles that add up to 90°.

Question #3:

Choose the pair of complementary angle measures.

37° and 53°

23° and 47°

86° and 94°

73° and 21°

The correct answer is 37° and 53°. Complementary angles are angles with measures that add up to 90°. Add the measures for each answer choice and choose the one that equals 90°.
$$37°+53°=90°$$
$$23°+47°=70°$$
$$86°+94°=180°$$
$$73°+21°=94°$$
37° and 53° are complementary angle measures.

Question #4:

What is the measure of an angle complementary to 48°?

132°

127°

42°

27°

The correct answer is 42°. Complementary angles add to 90°, so to find the complementary angle, subtract the known angle from 90°.
$$90°-48°=42°$$
The angle complementary to a 48° angle is 42°.

Question #5:

Choose the pair of complementary angle measures.

39° and 71°

17° and 43°

77° and 103°

21° and 69°

$$39°+71°=110°$$
$$17°+43°=60°$$
$$77°+103°=180°$$
$$21°+69°=90°$$