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

Complementary of two angles whose sum is 90

so 90 - 72 = 18

answer: smaller angle is 18

Complementary angles have to add up to 90°, so you know your larger angle (l) and smaller angle (s) can be used to say l+s=90. The question also states that the sum of the angles (e) is 72° greater than the difference (d), meaning e-72°=d. As we know the sum is 90°, we can conclude d=90°-72°=18°. As the difference would be d=l-s, we can determine d+s=l. We can then substitute this into our l+s=e equation to get e=d+s+s=d+2s, then we can solve for s to get e-d=2s = > (e-d) / 2=s, which we can then plug our values of e and d into to get s = (90°-18°) / 2=72°/2=36°. This makes your smallest angle 36°