If O be the circumcentre of a triangle PQR and ∠QOR

Home » Aptitude » Plane Geometry » Question

If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is

1. 65°
2. 50°
3. 55°
4. 60°

Correct Option: D

As per the given in question , we draw a figure of a triangle PQR with circumcentre O

Given , ∠QOR = 110°
∠OPR = 25°
∴ ∠QPR = 110° ÷ 2 = 55°
OR = OP
∴ ∠OPR = ∠PRO = 25°
∴ ∠OQR = ∠ORQ = 70 ÷ 2 = 35°
∴ ∠PRQ = 25° + 35° = 60°