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In triangle PQR, PQ = PR and angle Q = 65°. Side QR is produced to a point S. Find angle PRS in degrees.

Class 7The Triangle and its PropertiesTriangles
  • A65
  • B130
  • C115
  • D50

Step-by-Step Solution

PQ = PR makes the base angles equal, so angle R = angle Q = 65°. Angle PRS and angle PRQ form a linear pair, so angle PRS = 180 − 65 = 115°. Check with the exterior angle property: angle P = 180 − 65 − 65 = 50°, and angle P + angle Q = 50 + 65 = 115. Trap: adding the two base angles to get 130° — the exterior angle at R is made of angle P and angle Q, not angle Q counted twice.
Answer: C) 115

Key idea: Exterior angle property

Extend one side of a triangle past a vertex. The angle formed outside the triangle is the **exterior angle** at that vertex.

**Exterior angle = sum of the two opposite interior angles.**

So if the two non-adjacent interior angles are 50° and 60°, the exterior angle = 50° + 60° = 110°.

Why? The exterior angle and the adjacent interior angle form a linear pair (sum 180°), and the three interior angles also sum to 180°. Subtract: exterior = sum of the other two interior angles.

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