If PQR is an equilateral triangle inscribed in a circle and S and T are two points on the circle, find ∠QTR & ∠QSR.
Show answer & explanation
Correct answer: C
Explanation
In an equilateral triangle PQR, each interior angle is 60°; therefore, ∠QPR = 60°.
Angles subtended by the same arc QR at the circumference are equal; therefore, ∠QTR = ∠QPR = 60°.
For point S on the opposite arc, PQSR forms a cyclic quadrilateral.
The sum of opposite angles in a cyclic quadrilateral is 180°; therefore, ∠QSR = 180° − 60° = 120°.