Question : If the complement of an angle is one-fourth of its supplementary angle, then the angle is:
Option 1: 60°
Option 2: 30°
Option 3: 90°
Option 4: 120°
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Correct Answer: 60°
Solution :
Let $x$ be the angle. The complement of the angle is $(90°-x)$. The supplement of the angle is $(180°-x)$. According to the question, $(90-x)=\frac{1}{4}(180-x)$ ⇒ $360-4x=180-x$ ⇒ $3x=180$ $\therefore x = 60°$ Hence, the correct answer is 60°.
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