How to Find Complementary and Supplementary Angles? (+FREE Worksheet!)

In this article, we will introduce you to the rules of complementary and supplementary angles and how to use them to find the value of a missing angle.

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Definition of the Complementary and supplementary angles

  • Two angles with a sum of 90 degrees are called complementary angles.
  • Two angles with a sum of 180 degrees are Supplementary angles.

Examples

Complementary and supplementary angles – Example 1:

Find the missing angle.

Solution:

Notice that the two angles form a right angle. This means that the angles are complementary, and their sum is 90.
Then: \(18+x=90→x=90^\circ-18^\circ=72^\circ\) The missing angle is 72 degrees

Complementary and supplementary angles – Example 2:

Angles Q and S are supplementary. What is the measure of angle Q if angle S is 35 degrees?

Solution:

Q and S are supplementary \(→Q+S=180→Q+35=180→ Q =180-35=145\)

Complementary and supplementary angles – Example 3:

Find the missing angle.

Solution:

Notice that two angles form a straight angle when together. This means that the angles are supplementary and have a sum of \(180^\circ\).
\(x+43=180→x=180-43=137^\circ\)

Complementary and supplementary angles – Example 4:

Find the missing angle.

Solution:

Notice that two angles form a straight angle when together. This means that the angles are supplementary and have a sum of \(180^\circ\).
\(x+38=180→x=180-38=142^\circ\)

Exercises for Complementary and supplementary angles

Find the missing measurement in the pair of angles.

Find the missing measurement in the pair of angles.

1. \(\color{blue}{x=}\)

2.\(\color{blue}{x=}\)

3.\(\color{blue}{x=}\)

4.\(\color{blue}{x=}\)

5.The measure of an angle is \(31^°\). What is the measure of its complementary angle? __________

6.The measure of an angle is \(76^°\). What is the measure of its supplementary angle? __________

  1. \(\color{blue}{156^\circ}\)
  2. \(\color{blue}{15^\circ}\)
  3. \(\color{blue}{113^\circ}\)
  4. \(\color{blue}{46^\circ}\)
  5. \(\color{blue}{59^\circ}\)
  6. \(\color{blue}{104^\circ}\)

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