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# Complementary Angles

## Two angles that add to 90 degrees.

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Complementary Angles

What if you knew that two angles together made a right angle? After completing this Concept, you'll be able to use what you know about complementary angles to solve problems about these angles.

### Guidance

Two angles are complementary when they add up to . Complementary angles do not have to be congruent to each other, nor do they have to be next to each other.

#### Example A

The two angles below are complementary. . What is ?

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

#### Example B

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

Again, the two angles add up to . Make an equation.

However, this is not what the question asks for. You need to plug back into each expression to find each angle.

For : , so .

For : , so .

#### Example C

Name one pair of complementary angles in the diagram below.

One example is and .

Watch this video for help with the Examples above.

### Vocabulary

Two angles are complementary when they add up to .

### Guided Practice

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

1.

2.

3.

4.

### Practice

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

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

1. If , find .
2. If , find .

For 10-15, determine if the statement is true or false.

1. Complementary angles add up to .
2. Complementary angles are always .
3. Complementary angles are always next to each other.
4. Complementary angles add up to .
5. Two angles that make a right angle are complementary.
6. The two non-right angles in a right triangle are complementary.