Question

A triangle has two corners of angles `pi /12` and `(3pi)/4`. What are the complement and supplement of the third corner?

Answer 1

See explanation below

Explanation:

The sum of inner angles of a triangle is `pi` rads or `180` degrees

The data are provided in rads. Lets operate

Let `theta` the unknown angle in rads, then

`theta+pi/12+3pi/4=pi` then

`theta=pi-pi/12-3pi/4=pi/6`

The complement will be `pi/6+alpha=pi/2` or `alpha=pi/2-pi/6=pi/3`

The suplement will be `pi/6+beta=pi` or `beta=pi-pi/6=5pi/6`