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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 90. 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. mGHI=x. What is x?

Because the two angles are complementary, they add up to 90. Make an equation.

x+34=90x=56

Example B

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

Again, the two angles add up to 90. Make an equation.

8r+9+7r+515r+1415rr=90=90=765.1

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

For mGHI: 8(5.1)+9=49.8, so mGHI49.8.

For mJKL: 7(5.1)+5=40.7, so mJKL40.7.

Example C

Name one pair of complementary angles in the diagram below.

One example is INJ and JNK.

Watch this video for help with the Examples above.

CK-12 Foundation: Chapter1ComplementaryAnglesB

Vocabulary

Two angles are complementary when they add up to 90.

Guided Practice

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

  1. 45
  2. 82
  3. 19
  4. z

Answers:

1. 45

2. 8

3. 71

4. 90z

Interactive Practice

Practice

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

  1. 3
  2. 82
  3. 51
  4. 30
  5. 22
  6. (x+y)
  7. x

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

  1. If mINJ=60, find mKNJ.
  2. If mINJ=70, find mKNJ.

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

  1. Complementary angles add up to 180.
  2. Complementary angles are always 45.
  3. Complementary angles are always next to each other.
  4. Complementary angles add up to 90.
  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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