O is the center and the arc PQR subtends an angle of 240° at O. PQ is extended to A. Then ∠AQR is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 120°.
Given that
∠POR = 240°
The angle subtended at the center of a circle is twice the angle subtended at the circumference:
So, ∠PMR = 240°/2 = 120°
∠PMR + ∠PQR = 180° (Opposite angle of a cyclic quadrilateral)
⇒ 120° + ∠PQR = 180°
∠PQR = 60°
⇒ ∠AQR = 180° - 60° = 120°