# How do you find the complement and supplement of pi/12?

Mar 21, 2018

$\frac{5 \pi}{12}$ radians or 75 degrees (complement), $\frac{11 \pi}{12}$ radians or 165 degrees (supplement)

#### Explanation:

Complementary: angle measures add up to 90 degrees

Supplementary: angle measures add up to 180 degrees

Radians per full circle (360 degrees): $2 \pi$

Radians per half circle (180 degrees): $\pi$

Radians per quarter circle (90 degrees): $\frac{1}{2} \pi$

Complementary angle measure:

$x + \frac{\pi}{12} = \frac{1}{2} \pi \rightarrow$ $x$ represents the unknown angle measure

$\frac{12 x}{12} + \frac{\pi}{12} = \frac{6 \pi}{12}$

$12 x + \pi = 6 \pi$

$12 x = 5 \pi$

$x = \frac{5 \pi}{12} \rightarrow$ Complementary angle measure in radians

To convert the angle measure to degrees, divide by $\frac{\pi}{180}$

Supplementary angle measure:

$y + \frac{\pi}{12} = \pi \rightarrow$ $y$ represents the unknown angle measure

$\frac{12 y}{12} + \frac{\pi}{12} = \frac{12 \pi}{12}$

$12 y + \pi = 12 \pi$

$12 y = 11 \pi$

$y = \frac{11 \pi}{12} \rightarrow$ Supplementary angle measure in radians

To convert the angle measure to degrees, divide by $\frac{\pi}{180}$