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JAMB Mathematics 1982 Question 28

Question 28

Circle Theorems

In the above figure where PQRTU is a circle, |ST| = |RS| and angle TSR = 52°. Find the angle marked m.

Diagram for this question
  1. A.128°
  2. B.52°
  3. C.104°
  4. D.64°
  5. E.116°
Show the answer and explanation

Answer: E (116°)

Explanation

Triangle STR is isosceles, so <STR = (180° − 52°)/2 = 64° and <PTR = 180° − 64° = 116°. The angle m at U stands on the same chord PR in the same segment, so m = 116°.