In the diagram LMT is a straight line lf O is t... - WAEC Mathematics 2002 Question

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

44^o

46^o

52^o

70^o

correct option: b

< MNT = < MTN = 32°

< NMT = 180° - 2(32°) = 116°

< OMN + < NMT + < LMO = 180°

20° + 116° + < LMO = 180° \(\implies\) < LMO = 180° - 136° = 44°

< LMN = < LMO + < OMN

= 44° + 20° = 64°

< NOM = 180° - 2(20°) = 140°

< NLM = \(\frac{1}{2} \times < NOM = 70°\)

< LNM + < LMN + < NLM = 180°

< LNM + 64° + 70° = 180°

< LNM = 180° - 134° = 46°

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