Question

A triangle has two corners of angles `pi /12` and `pi/8`. What are the complement and supplement of the third corner?

Answer 1

The supplement of the third angle is `5/24pi`
It does not have a complement.

Explanation:

The sum of all 3 angles in any triangle is `pi` (or `180^0`)

So we find the third angle with this equation:

`pi/12 + pi/8 + x = pi`
`x=pi - 2/24pi - 3/24pi`
`x=19/24pi`

Two angles are complementary if the sum of the two angles adds up to `pi/2` (or `90^0`)

But this is an obtuse angle: `19/24pi > pi/2`
so it does not have a complement.

Two angles are supplementary if the sum of the two angles adds up to `pi` (or `180^0`)
`19/24pi + S = pi`
`S = pi - 19/24pi`

The supplement angle is: `S = 5/24pi`