Question

The sum of the measures of two complementary angles exceeds the difference of their measures by 72°. Find the measure of the smaller angle. A. 18° B. 36° C. 54° D. 58°

Answer 1

First we need to define our conditions. Since the angles are complimentary, the sum of the angles must be equal to 90 degrees.

let x = first angle
y = second angle

x + y = 90

from the second condition in the problem 

x + y =72 + x -y
solving for x

x= 54

therefore the shorter side is 90 - 54 = y

y = 36 degree, the shorter side