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.
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Correct Answer: Option B
Explanation:
< 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°
< 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°