The sum of the measures of two complementary angles exceeds the difference of their measures by 72°. Find the measure of the smaller angle.

Question

anonymous · Answer

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