Question

A triangle has two corners of angles `(pi )/4` and `(2pi)/3`. What are the complement and supplement of the third corner?

Answer 1

Complementary angle is `(5pi)/12` and supplementary angle is `(11pi)/12`

Explanation:

The two angles of the triangle are `pi/4` and `2pi/3`.

As sum of angles of a triangle is `pi`, the third angle is

`pi-pi/4-2pi/3=(12pi)/12-(3pi)/12-(8pi)/12=pi/12`

Now complementary angles add up to `pi/2` and supplementary angles add up to `pi`.

Hence complementary angle of third angle `pi/12` is `pi/2-pi/12=(6pi)/12-pi/12=(5pi)/12`

and supplementary angle of third angle `pi/12` is `pi-pi/12=(12pi)/12-pi/12=(11pi)/12`