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Supplementary Angles

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What if you were given two supplementary angles? How would you determine their angle measures? After completing this Concept, you'll be able to use the definition of supplementary angles to solve problems like this one.

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CK-12 Foundation: Chapter1SupplementaryAnglesA

James Sousa: Supplementary Angles

Guidance

Two angles are supplementary when they add up to 180^\circ . Supplementary angles do not have to be congruent or touching.

Example A

The two angles below are supplementary. If m \angle MNO = 78^\circ what is m \angle PQR ?

Set up an equation.

78^\circ + m \angle PQR = 180^\circ\\m \angle PQR = 102^\circ

Example B

What are the measures of two congruent, supplementary angles?

Supplementary angles add up to 180^\circ . Congruent angles have the same measure. Divide 180^\circ by 2, to find the measure of each angle.

180^\circ \div 2 = 90^\circ

So, two congruent, supplementary angles are right angles, or 90^\circ .

Example C

Name one pair of supplementary angles in the diagram below.

One example is   \angle INM and  \angle MNL .

Watch this video for help with the Examples above.

CK-12 Foundation: Chapter1SupplementaryAnglesB

Vocabulary

Two angles are supplementary when they add up to 180^\circ .

Guided Practice

Find the measure of an angle that is supplementary to \angle ABC if m \angle ABC is

1. 45^\circ

2. 118^\circ

3. 32^\circ

4. x^\circ

Answers:

1. 135^\circ

2. 62^\circ

3. 148^\circ

4. 180-x^\circ

Interactive Practice

Practice

Find the measure of an angle that is supplementary to \angle ABC if m\angle ABC is:

  1. 112^\circ
  2. 15^\circ
  3. 97^\circ
  4. 81^\circ
  5. 57^\circ
  6. (x-y)^\circ
  7. (x+y)^\circ

Use the diagram below for exercises 8-9. Note that \overline{NK} \perp \overleftrightarrow{IL} .

  1. Name another pair of supplementary angles.
  1. If m\angle INJ = 63^\circ , find m\angle JNL .

For exercises 10-13, determine if the statement is true or false.

  1. Supplementary angles add up to 180^\circ .
  2. Two angles on a straight line are supplementary angles.
  3. To be supplementary, two angles must be touching.
  4. It's possible for two angles in a triangle to be supplementary.

For 14-15, find the value of x .

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