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JAMB Mathematics 1985 Question 37

Question 37

Circle Theorems

In the figure above, MNQP is a cyclic quadrilateral. MN and PQ are produced to meet at X and NQ and MP are produced to meet at Y. If MNQ = 86° and NQP = 122°, find (x°, y°).

Diagram for this question
  1. A.(28°, 36°)
  2. B.(36°, 28°)
  3. C.(43°, 61°)
  4. D.(61°, 43°)
  5. E.(36°, 43°).
Show the answer and explanation

Answer: A ((28°, 36°))

Explanation

Opposite angles of a cyclic quadrilateral add to 180°, so <M = 58° and <MPQ = 94°. In triangle MXP, x = 180° − 58° − 94° = 28°. In triangle MNY, y = 180° − 58° − 86° = 36°.