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In the diagram, |PS| is a diameter of circle PQRS. |PQ| = |QR| and ∠RSP...

Mathematics
WAEC 1994

In the diagram, |PS| is a diameter of circle PQRS. |PQ| = |QR| and ∠RSP = 74º. Find ∠QPS

  • A. 32o
  • B. 37o
  • C. 48o
  • D. 53o
  • E. 74o
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Correct Answer: Option D
Explanation

Join PR.

< PQR = 180º - 74º = 106º

<PRQ = \(\frac{180 - 106}{2}\) = 37º ⇒ < QRS = 37º + 90º = 127º

< QPS = 180 - 127 = 53º

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