# Complementary Angles

## Two angles that add to 90 degrees.

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Complementary Angles

### Complementary Angles

Two angles are complementary if they add up to . Complementary angles do not have to be congruent or adjacent.

What if you were given two angles of unknown size and were told they are complementary? How would you determine their angle measures?

### Examples

#### Example 1

Find the measure of an angle that is complementary to if is .

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#### Example 2

Find the measure of an angle that is complementary to if  is

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#### Example 3

The two angles below are complementary. . What is ?

Because the two angles are complementary, they add up to . Make an equation.

#### Example 4

The two angles below are complementary. Find the measure of each angle.

The two angles add up to . Make an equation.

However, you need to find each angle. Plug back into each expression.

#### Example 5

Find the measure of an angle that is complementary to if is .

Because complementary angles have to add up to , the other angle must be .

### Review

Find the measure of an angle that is complementary to if is:

Use the diagram below for exercises 8-9. Note that .

1. Name two complementary angles.
1. If , find .

For 10-11, determine if the statement is true or false.

1. Complementary angles add up to .
2. Complementary angles are always .

To see the Review answers, open this PDF file and look for section 1.7.

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complementary angles Two angles are complementary if they add up to $90^\circ$.