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

Given : ∠PQR = 40° and ∠QRP = 60° 

To find : ∠QOR = $$\theta$$ = ?

Solution : In $$\triangle$$ PQR,

=> ∠ PQR + ∠ QRP + ∠QPR = $$180^\circ$$

=> $$40^\circ+60^\circ+\angle QPR=180^\circ$$

=> $$\angle QPR=180^\circ-100^\circ=80^\circ$$

Angle subtended by an arc at the centre is double the angle subtended by it at an other point on the circle,

=> ∠ QOR = $$2 \times \angle QPR$$

=> $$\theta=2 \times 80^\circ=160^\circ$$

=> Ans - (D)