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

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Mathematics WAEC 2004

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

  • 35o
  • 45o
  • 55o checkmark
  • 70o

The correct answer is: 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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