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In the diagram, O is the centre of the circle ∠PQR = 75o, ∠OPS =...

Mathematics
WAEC 1999

In the diagram, O is the centre of the circle ∠PQR = 75o, ∠OPS = yo and \(\bar{OR}\) is parallel to \(\bar{PS}\). Find y

  • A. 15
  • B. 30
  • C. 45
  • D. 75
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Correct Answer: Option B
Explanation

In the diagram:

<POR = 2 x 75 = 150º (< at centre = 2 x < at circumference)

<PSR = 180 - 75º = 105º

<ORS = 180 - 105º = 75º(adjacent <s)

y + 150º + 75º + 105º = 360º (sum of <s in a quadrilateral)

y = 360º - 330º = 30º


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