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Supplementary Angles

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Supplementary Angles

What if you were given two angles of unknown size and were told they are supplementary? 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.

Watch This

CK-12 Basic Geometric Definitions

Watch this video beginning at around the 3:20 mark.

James Sousa: Angle Basics--Supplementary Angles

Then watch the second part of this video.

James Sousa: Supplementary Angles

Guidance

Two angles are supplementary if they add up to 180^\circ . Supplementary angles do not have to be congruent or next to each other .

Example A

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

Set up an equation. However, instead of equaling 90^\circ , now the sum is 180^\circ .

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. So, 180^\circ \div 2 = 90^\circ , which means two congruent, supplementary angles are right angles, or 90^\circ .

Example C

Find the measure of an angle that is a supplementary to \angle MRS if  m\angle  MRS is  70^\circ .

Because supplementary angles have to add up to 180^\circ , the other angle must be 180^\circ-70^\circ=110^\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. 2^\circ

Answers:

1. Because supplementary angles have to add up to 180^\circ , the other angle must be 180^\circ-45^\circ=135^\circ .

2. Because supplementary angles have to add up to 180^\circ , the other angle must be 180^\circ-118^\circ=62^\circ .

3. Because supplementary angles have to add up to 180^\circ , the other angle must be 180^\circ-32^\circ=148^\circ .

4. Because supplementary angles have to add up to 180^\circ , the other angle must be 180^\circ-2^\circ=178^\circ .

Practice

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

  1. 114^\circ
  2. 11^\circ
  3. 91^\circ
  4. 84^\circ
  5. 57^\circ
  6. x^\circ
  7. (x+y)^\circ

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

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

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

  1. Supplementary angles add up to 180^\circ

For 11-12, find the value of x .

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