Problem 12 · 2019 Math Kangaroo
Medium
Geometry & Measurement
symmetry
The following is known about triangle PSQ: angle QPS = 20°. The triangle PSQ has been split into two smaller triangles by the line QR, as shown. It is known that PQ = PR = QS. How big is the angle RQS?
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Answer: B — 60°
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Hint 1 of 2
PQ = PR makes one isosceles triangle; use its base angles.
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Hint 2 of 2
Then chase angles into triangle QRS where QS = PR.
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Approach: isosceles angle chase
- In triangle PQR, PQ = PR and the apex angle at P is 20°, so the base angles are each (180−20)/2 = 80°.
- Angle QRS is the supplement of 80° along line PS, namely 100°.
- With QS = PR the remaining triangle forces angle RQS = 60°.
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