Complementary angles are two angles whose measures add up to 90° (or [latex]\dfrac{\pi}{2}[/latex] radians).Supplementary angles are two angles whose measures add up to 180° (or [latex]\pi[/latex] radians).
Pro Tip: An angle can only have a complement if it measures less than 90°. An angle of 90° or greater has no complement.
Find the complement of [latex]37°[/latex].
Find the supplement of [latex]125°[/latex].
[latex]\begin{aligned} \text{Complement} &= 90° - 37° \ &= 53° \end{aligned}[/latex]The complement of [latex]37°[/latex] is [latex]53°[/latex].
We can verify: [latex]37° + 53° = 90°[/latex]
[latex]\begin{aligned} \text{Supplement} &= 180° - 125° \ &= 55° \end{aligned}[/latex]
The supplement of [latex]125°[/latex] is [latex]55°[/latex].We can verify: [latex]125° + 55° = 180°[/latex] ✓
Finding Complements and Supplements in Radians
When working with radians, complementary angles sum to [latex]\dfrac{\pi}{2}[/latex] radians (which equals 90°) and supplementary angles sum to [latex]\dfrac{\pi}[/latex] radians (which equals 180°)
Find the complement of [latex]\dfrac{\pi}{6}[/latex] radians.
Find the supplement of [latex]\dfrac{2\pi}{3}[/latex] radians.