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Complementary Angles (Mathematics Lesson)

Complementary Angles

Complementary angles are two angles which add up to a right angle.



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 angle complements the 53° angle below?



Step 1: The 53° angle and θ are complementary angles. They add up to 90°.
53° + θ = 90°.

Step 2: Subtract the 53° angle from 90°.
θ = 90° - 53° = 37°.

The complementary angle is 37°.

Another Real Example of Complementary Angles

The slider below shows a real example of complementary angles in mathematics, where two angles in a right triangle are complementary:
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Top Tip
WHAT TYPES OF ANGLES ARE COMPLEMENTARY?

Complementary angles form a Corner.

Note
WHAT'S IN A NAME?

Complementary comes from the Latin word 'complementum' meaning "filled up".

This is because an acute angle is filled up to form a right angle.

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.