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

Let x and y be the two complementary angles

since they are complementary, we know they add to 90 degrees, so

x+y = 90

Answer 2

we are told that "The sum of the measures of two complementary angles exceeds the difference of their measures by 72", so

x+y = x-y + 72

y = -y + 72

y + y = 72

2y = 72

y = ???

Answer 3

Complementary angles have measures that add up to 90.
Let one angle have measure x. The other angle has measure 90 - x

Sum of measures: x + (90 - x)
Difference of their measures: x - (90 - x)
Sum of measures exceeds diff of measures by 72:
x + (90 + x) = x - (90 - x) + 72
Solve for x

Answer 4

so whats the answer

Answer 5

x + (90 - x) = x - (90 - x) + 72
x - x + 90 = x - 90 + x + 72
90 = 2x - 18
108 = 2x
54 = x

90 - 54 = 36

The smaller angle measure 36 degrees.