Question

Find (if possible) the complement and the supplement of each angle. (if not possible, enter impossible.) (a) π 10 complement radians supplement radians (b) 9π 10 complement radians supplement radians

Answer 1

In this question, we have to find the complement and supplement of the given angles .

Complementary angles are those angles whose sum is 90 degree and supplementary angles are those angles whose sum is 180 degree.

So to find the complement and supplement angles, we need to subtract the given angles from pi/2 and pi respectively .

a.

$\frac{ \pi}{10} \\ complement  \ angle = \frac{ \pi}{2} - \frac{ \pi}{10}     \\                             = \frac{4 \pi}{10} = \frac{ 2 \pi}{5} \\ Supplement  \ angle = \pi - \frac{ \pi}{10} = \frac{9 \pi}{10}$

b.

$\frac{9 \pi}{10} \\ Complement \ angle = \frac{ \pi}{2} - \frac{9 \pi}{10} = \frac{-4 \pi}{10} = -\frac{2 \pi}{5} \\ Supplement \ angle = \pi - \frac{9 \pi}{10} = \frac{ \pi}{10}$