A school flag triangular pennant PQR is isoceles with PQ = PR. The apex angle ∠QPR at the top is 50°. The base QR is extended past R to a point S along the flagpole edge. What is the size of the exterior angle ∠PRS?
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Worked Solution
Step 1: Use the isoceles property. Because PQ = PR, the base angles are equal: ∠PQR = ∠PRQ.
Step 2: Apply the triangle angle sum. ∠PQR + ∠PRQ + ∠QPR = 180°, so 2 × ∠PRQ + 50° = 180°.
Step 3: Solve for the base angle. 2 × ∠PRQ = 180° − 50° = 130°, so ∠PRQ = 130° ÷ 2 = 65°.
Step 4: Find the exterior angle on the straight line QRS. ∠PRQ + ∠PRS = 180°, so ∠PRS = 180° − 65° = 115°.
Check (reverse): 115° + 65° = 180° ✓ (linear pair); 65° + 65° + 50° = 180° ✓ (triangle sum).
Final answer: ∠PRS = 115°.
Answer: 115°
Correct answer: 115°
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