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

Answer 1

Complementary angles are pair of two non-right angles whose sum is equal to 90°

Let the two complementary angles be : Δ and Ф

Given : Sum of the measures of two complementary angles exceed the difference of their measures by 72°

$:\implies$  Δ + Ф - 72° = Δ - Ф

$:\implies$  2Ф = 72°

$:\implies$  Ф = 36°

As Δ and Ф are complementary, their sum should be equal to 90°

$:\implies$  Δ + 36° = 90°

$:\implies$  Δ = 90° - 36°

$:\implies$  Δ = 54°

So, Complementary angles are 54° and 36°

Answer : The Measure of the Smaller Angle is 36°