Question

A triangle has two corners of angles `pi /6` and `(3pi)/8`. What are the complement and supplement of the third corner?

Answer 1

Complement of third angle is `pi/24`

and supplement of third angle is `(13pi)/24`

Explanation:

As the two corners of angles are `pi/6` and `(3pi)/8` and sum of angles of a triangle is `pi`

the third angle is `color(white)(XXXX)pi-pi/6-(3pi)/8`

= `(24pi-4pi-9pi)/24=(11pi)/24`

Sum of complementary angle is `pi/2` and sum of supplementary angle is `pi`

Hence complement of third angle, which is `(11pi)/24` is

`pi/2-(11pi)/24=(12pi-11pi)/24=pi/24`

and supplement of third angle is

`pi-(11pi)/24=(24pi-11pi)/24=(13pi)/24`