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

1 Answer
Jun 29, 2018

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