Question

A triangle has two corners of angles `pi /8` and `(5pi)/8`. What are the complement and supplement of the third corner?

Answer 1

I'm assuming you want answers in radians, so here they are:
Complement = `pi/4` radians
Supplement = `(3pi)/4` radians

Explanation:

Since we are working with a denominator of 8, let's convert our basic radian measures to a denominator of 8 to make this more easy to work with.

90 degrees = `(4pi)/8` radians
180 degrees = `(8pi)/8` radians

The supplement is quite easy to find:

All 3 angles of a triangle add up to 180 degrees (`(8pi)/8` radians)
Supplementary angles add up to 180 degrees (`(8pi)/8` radians)
Therefore, the supplement of the angle at the 3rd corner would simply be the sum of the measures of the other two, which would be `(6pi)/8`, or `(3pi)/4`.

The complement is similar. We can easily see that the measure of the unmentioned angle is `(2pi)/8` radians, and therefore its complement is `(4pi)/8 - (2pi)/8`, which is equal to `(2pi)/8`, or `pi/4`.