In the diagram, PR is a diameter, ∠PRQ = (3x-8)o and ∠RPQ = (2y-7)o. s x in terms of y

  • A \(x=\frac{75-2y}{3}\)
  • B \(x=\frac{105-3y}{2}\)
  • C \(x=\frac{105-2y}{3}\)
  • D \(x=\frac{75-3y}{2}\)
waec 2005mathematics

The correct answer is C. \(x=\frac{105-2y}{3}\)

180 = ∠RPQ + ∠PRQ + ∠PQR Since PQR = 90 (theorem: angle in a semi circle)

180 = ∠RPQ + ∠PRQ + 90 => 180o = (3x-8)o+(2y-7)o+90o; 90+8+7 = 3x+2y =>\(\frac{105-2y}{3}=x\)

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