JAMB - Mathematics (1979 - No. 21)

PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If < PQS = 15o find < QRS
75o
37\(\frac{1}{2}\)o
127\(\frac{1}{2}\)o
105o

Explanation

PSO = 90o(angle in a semicircle)

SPO = 180o - (90o + 15o) = 75o

< QRS = 108o - 75o

= 105o(opposite angles in cyclic quadrilateral are supplementary)

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