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WAEC Mathematics 2002 Question 50

Question 50

Circle Theorems

In the diagram, LMT is a straight line. If O is the centre of circle LMN, ∠OMN = 20°, ∠LTN = 32° and |NM| = |MT|, find ∠LNM.

Diagram for this question
  1. A.44°
  2. B.46°
  3. C.52°
  4. D.70°
Show the answer and explanation

Answer: B (46°)

Explanation

NM = MT gives ∠MNT = 32°, so ∠NMT = 116° and ∠LMN = 64°. OM = ON gives ∠MON = 140°, so ∠MLN = 70°. Then ∠LNM = 180 − 64 − 70 = 46°.