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In the diagram, O is the centre of the circle where OS//QR and ∠SOR =...

Mathematics
WAEC 2004

In the diagram, O is the centre of the circle where OS//QR and ∠SOR = 35º. Find the value of  ∠QPR.

  • A. 35o
  • B. 45o
  • C. 55o
  • D. 70o
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Correct Answer: Option C
Explanation

∠SOR = ∠ORQ alternate angle.
Also ∠OQR = ∠OQR (Base angle of isosceles)
∠QOR = 180 – 2(35º) = 180 - 70º = 110º, ∠QPR = 1/2QOR = 1/2(110º) ∠QPR = 55º (theorem angle at center is twice angle at circumference)


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