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