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

 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°

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