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JAMB Mathematics 2002 Question 27

Question 27

Angles and Polygons

In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = 72°, find x.

Diagram for this question
  1. A.36°
  2. B.18°
  3. C.72°
  4. D.24°
Show the answer and explanation

Answer: D (24°)

Explanation

Triangle PQS is isosceles, so ∠QSP = x and the exterior angle ∠SQR = 2x. Triangle QSR is isosceles, so ∠SRQ = 2x. ∠RST is exterior to triangle PRS, so 3x = 72° and x = 24°.