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°

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°

directrix · Answer

@veronstew

Let x be one of the two complementary angles

Because complementary angle measures sum to 90, then

90 - x is the other angle.

directrix · Answer

Sum is 90

Difference:  [ x - (90 - x) ]

Sum exceeds difference by 72:

90 - [x - (90-x)] = 72

Solve for x.

Then, determine which is smaller: x or 90 - x. @veronstew