How to Find Complementary and Supplementary Angles? (+FREE Worksheet!)
Complementary and supplementary angles, Example 2:
Complementary and supplementary angles, Example 3:
Two angles are complementary when they add to 90 degrees and supplementary when they add to 180. Angles on a straight line are supplementary; the two acute angles in a right triangle are complementary. Below: how to find the missing angle in each case, with worked examples and a free worksheet.
Supplementary, Complementary, and Vertical Angles: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- Label the diagramWrite each given measurement on the figure.
- Choose the formulaMatch the formula to distance, midpoint, area, volume, or angle relationships.
- Check unitsUse linear, square, or cubic units as appropriate.
Worked examples
Complementary angles
- Complements total 90 degrees.
- Subtract 37 from 90.
- Label the angle.
Supplementary angles
- Supplements total 180 degrees.
- Subtract 118 from 180.
- Label the angle.
Try one before moving on
Supplementary, Complementary, and Vertical Angles: pop-up practice
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? __________
- \(\color{blue}{156^\circ}\)
- \(\color{blue}{15^\circ}\)
- \(\color{blue}{113^\circ}\)
- \(\color{blue}{46^\circ}\)
- \(\color{blue}{59^\circ}\)
- \(\color{blue}{104^\circ}\)
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