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JAMB Mathematics 2005 Question 27

Question 27

Circle Theorems

In the diagram above, O is the centre of the circle, ∠UOT = 70° and ∠RST = 100°. Calculate ∠RUO.

Diagram for this question
  1. A.20°
  2. B.25°
  3. C.50°
  4. D.80°
Show the answer and explanation

Answer: B (25°)

Explanation

OU = OT, so ∠OUT = (180° − 70°)/2 = 55°. RSTU is cyclic, so ∠RUT = 180° − 100° = 80°. Then ∠RUO = 80° − 55° = 25°.