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JAMB Mathematics 1979 Question 25

Question 25

Circle Theorems

PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If <PQS = 15° find <QRS

  1. A.75°
  2. B.37½°
  3. C.127½°
  4. D.105°
  5. E.None of the above.
Show the answer and explanation

Answer: D (105°)

Explanation

The angle in a semicircle is 90°, so <PSQ = 90° and <SPQ = 75°. Opposite angles of a cyclic quadrilateral add to 180°, so <QRS = 105°.