Question

A triangle has two corners of angles `pi /6` and `(3pi)/4`. What are the complement and supplement of the third corner?

Answer 1

Complement of the third corner is `(5pi)/12` and supplement of the third corner is `(11pi)/12`.

Explanation:

As sum of the angles of a triangle is `pi` and two angles are `pi/6` and `(3pi)/4`, the third angle is given by

`pi-pi/6-(3pi)/4=(12pi-2pi-9pi)/12=pi/12`

As sum of two complementary angles is `pi/2`, complementary angle of third angle is `pi/2-pi/12=(6pi-pi)/12=(5pi)/12`

As sum of two supplementary angles is `pi`, supplementary angle of third ange is `pi-pi/12=(11pi)/12`.