Question : $\triangle \mathrm{PQR}$ is an equilateral triangle inscribed in a circle. $\mathrm{S}$ is any point on the arc $\mathrm{QR}$. Find the measure of $\angle \mathrm{PSQ}$.
Option 1: $30^{\circ}$
Option 2: $60^{\circ}$
Option 3: $90^{\circ}$
Option 4: $45^{\circ}$
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Correct Answer: $60^{\circ}$
Solution :
Since $\triangle PQR$ is an equilateral triangle,
$\angle PQR = \angle QRP = \angle RPQ = 60°$
Angles subtended by a chord on the same side of a circle are equal.
Here, $\angle QRP$ and $\angle PSQ$ are angles subtended on the circle by chord $PQ$.
So, $\angle PSQ = \angle QRP = 60°$
Hence, the correct answer is $60^{\circ}$.
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