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WAEC Mathematics 2023 Question 30

Question 30

Circle Theorems

In the diagram, NR is a diameter, ∠MNR = x° and ∠SRN = (5x + 20)°. Find the value of 2x.

Diagram for this question
  1. A.20°
  2. B.35°
  3. C.42°
  4. D.90°
Show the answer and explanation

Answer: B (35°)

Explanation

∠NMR = 90° (angle in a semicircle), so ∠NRM = 90° − x. S, R and M lie on a straight line, so ∠SRN = 180° − (90° − x) = 90° + x. Then 5x + 20 = 90 + x gives x = 17.5 and 2x = 35°.