Question
Find the angle whose complement is one-third of its supplement.
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Answer
Let the measure of the required angle be xº. Then, the measure of its complement = (90 - x)º. And the measure of its supplement = (180 - x)º. Therefore,$(90 - \text{x}) = \frac{1}{3}(180-\text{x})$
⇒ 3(90 - x) = (180 - x) ⇒ 270 - 3x = 180 - x ⇒ 2x = 90 ⇒ x = 45 Hence, the measure of the required angle is 45º.
⇒ 3(90 - x) = (180 - x) ⇒ 270 - 3x = 180 - x ⇒ 2x = 90 ⇒ x = 45 Hence, the measure of the required angle is 45º.
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