Question

A triangle has two corners of angles `pi /8` and `(pi)/2`. What are the complement and supplement of the third corner?

Answer 1

Complementary angle of third angle is `pi/8` and supplementary angle of third angle is `(5pi)/8`

Explanation:

As the two angles are `pi/8` and `pi/2`, the third angle is

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

As complementary angles add up to `pi/2`,

its complementary is `pi/2-(3pi)/8=(4pi)/8-(3pi)/8=pi/8`

As supplementary angles add up to `pi`,

its complementary is `pi-(3pi)/8=(8pi)/8-(3pi)/8=(5pi)/8`