Question

(y − 20)^° and (y + 30)^° are the measures of complementary angles. Find the measure of each angle.

Answer 1

The sum of two complementary angles is 90°

∴ (y − 20)^° + (y + 30)^° = 90^°

⇒ y + y + 30 − 20  = 90

⇒ 2y + 10 = 90

⇒ 2y = 90 − 10

⇒ 2y = 80

⇒ y = `80/2`

⇒ y = 40

Measure of first angle = (y – 20)^°

= (40 – 20)^°

= 20^°

Measure of second angle = (y + 30)^°

= (40 + 30)^°

= 70^°

Hence, the measures of the two angles are 20^° and 70^°.