The Lesson

Complementary angles are two angles which add up to a right angle (90°). Two angles that add to 90° are are said to complement each other.

A Real Example of Complementary Angles

Angles of 30° and 60° are complementary angles.
30° + 60° = 90°

How to Find a Complementary Angle

Question

What is the missing angle θ below?

Step-by-Step:

1

The 53° angle and θ are complementary angles. They add up to 90°.
53° + θ = 90°

2

Subtract the 53° angle from 90°.
θ = 90° − 53° = 37°

Answer:

The missing angle θ is 37°.

Lesson Slides

The slider below shows another real example of complementary angles. Open the slider in a new tab

Top Tip

What Types of Angles Are Complementary?

Complementary angles form a Corner.

Note

What's In an Name?

Complementary comes from the Latin word "complementum" meaning "fill up, complete, supply. This is because an acute angle is filled up to form a right angle. We get the word "complete" from the same root. Don't confuse a complementary angle with a complimentary angle; which would be a free angle or an angle giving praise.

Complementary Angles Are Acute Angles

Both complementary angles are less than 90°, and so are acute angles.