Question
Find the angle whose complement is one-third of its supplement.
✓
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.
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.
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