Question : PQR is an equilateral triangle inscribed in a circle. S is any point on the arc QR. Measure of $\frac{1}{2} \angle \mathrm{PSQ}$ is:
Option 1: 20°
Option 2: 15°
Option 3: 30°
Option 4: 60°
Answer (1)
25th Jan, 2024
Correct Answer: 30°
Solution :
Since PQR is an equilateral triangle inscribed in a circle, each of its angles is 60°.
$\angle PSQ=\angle QRP = $ 60° (Angles in the same segment)
$\frac{1}{2}\times \angle PSQ=\frac{60°}{2}=30°$
Hence, the correct answer is 30°.
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