Points P, Q and R are on a circle such that∠PQR = 40°

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Points P, Q and R are on a circle such that∠PQR = 40° and ∠QRP = 60°. Then the subtended angle by arc QR at the centre is :

1. 80°
2. 120°
3. 140°
4. 160°

Correct Option: D

According to question , we draw a figure of a circle with centre O ,

In ∆ PQR,
∠PQR = 40° ; ∠QRP = 60°
∴ ∠QPR = 180° – 60° – 40° = 80°
∴ Angle subtended at the circumference by arc QR = 80°
∴ Angle subtended at the centre by arc QR = ∠QOR = 2∠QPR = 2 × 80° = 160°