The measure of the supplement of an angle is 5 times that of its complement. Find the measure of the complement

Question

measure of the supplement of an angle is 5 times that of its complement. Find the measure of the complement

Answer 1

Supplementary angles add up to 180 degrees.

Complementary angles add up to 90 degrees.

 

X is the angle.

180-x is the supplement

90-x is the complement

 

(180-x) = (5)(90-x)

solve for x, then find 180-x

180 - x = 450-5x

4x = 270

x = 67.5

 

Supplement = 180-67.5 =112.5