## Complementary Angles

Complementary comes from Latin ** completum **meaning “

**“, because the right angle is thought of as being a complete angle.**

**completed**Table of Contents

## Definition of Complementary Angles

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

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 90^{o}(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.

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

## Complementary Angles In Right Angled Triangle

An angle measuring 90^{o} 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.

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

Since a right angle doesn’t need another angle to complete the 90^{o}, 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 90^{o}.

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

2 angles measuring 45^{o} are complementary.

Angles measuring 40^{o} and 50^{o} are a complementary pair

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

## Complementary vs Supplementary

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

How to remember which is which? Easy! Think:

“C” of Complementary | stands for “Corner” (a Right Angle) |

“S” of Supplementary | stands for “Straight” (a straight line) |