ΔPQR is an equilateral triangle inscribed in a circle. S is any point on the arc QR. Find the measure of ∠PSQ. 

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SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 3)
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  1. 30°
  2. 60°
  3. 90°
  4. 45°

Answer (Detailed Solution Below)

Option 2 : 60°
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Detailed Solution

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Given:

ΔPQR is an equilateral triangle inscribed in a circle.

S is any point on the arc QR.

Concept used:

Each of the angles of an equilateral triangle is equal and 60° 

The angles subtended by an arc in the same segment of a circle are equal.

Calculation:

Both ∠PRQ and ∠PSQ are in the subtended by the arc PQ in the same segment, so

∠PRQ = ∠PSQ = 60°

 ∴ The correct option is 2

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