In the diagram, PR is a diameter, ∠PRQ = (3x-8)° and ∠RPQ = (2y-7)°. Find...

MATHEMATICS

WAEC 2005

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

A. \(x=\frac{75-2y}{3}\)
B. \(x=\frac{105-3y}{2}\)
C. \(x=\frac{105-2y}{3}\)
D. \(x=\frac{75-3y}{2}\)

Correct Answer: C. \(x=\frac{105-2y}{3}\)

Explanation

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

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

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