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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.

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CK-12 Foundation: Chapter1ComplementaryAnglesA

James Sousa: Complementary 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.

CK-12 Foundation: Chapter1ComplementaryAnglesB

Vocabulary

Two angles are complementary when they add up to .

Guided Practice

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

Answers:

1.

2.

3.

4.

Interactive Practice

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.

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