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

1 Answer
Jan 13, 2017

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.