Complementary Angles

Complementary comes from Latin completum meaning “completed“, because the right angle is thought of as being a complete angle.

Definition of Complementary Angles

Complementary angles are 2 angles whose measures add up to 90o. For example 2 puzzle pieces that form one 90o angle when they are put together.

Complementary Angles

Complementary angles are always in a pair. One angle is complementary to the other or One angle is the complement of the other.

2 angles are Complementary when they add up to 90o (a Right Angle).

These 2 angles (∠AOB and ∠AOC) are Complementary Angles, because they add up to 90° (30°+60°).

But the angles don’t have to be together.

Complementary Angles Each Other

These 2 are complementary because 30° + 60° = 90°

Complementary Angles In Right Angled Triangle

An angle measuring 90o by itself is called a right angle.

In a right angled triangle, the two non-right angles are complementary, because in a triangle the three angles add to 180°, and 90° has already been taken by the right angle.

Complementary Angles Right Triangle

When two angles add to 90°, we say they “Complement” each other.

Since a right angle doesn’t need another angle to complete the 90o, it doesn’t have a complement and can’t be called a complement by itself.

3 or more angles are also not called complementary, even if their measures to add up to 90o.

Complementary angles always have positive measures. Each of the complements must be acute (less than 90o), because their measures add up to 90o. 2 pizza pieces that together form a right angle can be any combination of 2 positive numbers that add up to 90o.

Examples

2 angles measuring 45o are complementary.

Angles measuring 40o and 50o are a complementary pair

An angle measuring 2o would the complement to an angle measuring 88o.

Complementary vs Supplementary

A related idea is Supplementary Angles – those add up to 180°

How to remember which is which? Easy! Think:

“C” of Complementarystands for “Corner” (a Right Angle)
“S” of Supplementarystands for “Straight” (a straight line)

Learn More

How To Find if Triangles are Congruent

Adjacent Angles

Alternate Exterior Angles

Alternate Interior Angles

Geometry Index

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