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JAMB Mathematics 1981 Question 15

Question 15

Circle Theorems

In the figure above, the chords XY and ZW are produced to meet at T such that YT = WT, ZYW = 40° and YTW = 30°. What is YXW?

Diagram for this question
  1. A.50°
  2. B.75°
  3. C.35°
  4. D.115°
  5. E.30°.
Show the answer and explanation

Answer: C (35°)

Explanation

Triangle YTW is isosceles, so <TWY = 75°. The exterior angle of cyclic quadrilateral XYWZ at W equals the opposite interior angle: <YXZ = 75°. <WXZ = <WYZ = 40° (same segment), so <YXW = 75° − 40° = 35°.