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GCE Mathematics 1989 Question 14

Question 14

Triangles and Quadrilaterals

In the diagram below, ∠SPR = p and ∠SQR = 2x. Find x in terms of p.

Diagram for this question
  1. A.x = p + 2
  2. B.x = p − 2
  3. C.x = p2
  4. D.x = p/2
  5. E.x = 2p
Show the answer and explanation

Answer: D (x = p/2)

Explanation

∠SPR and ∠SQR stand on the same arc SR, so they are equal: 2x = p, giving x = p/2.