In the diagram, LMT is a straight line. lf O is the centre of circle LMN, OMN = 20^\circ, LTN = 32^\circ and |NM| = |MT|, find LNM.
Attached Figure / Diagram
A
44o
B
46o
C
52o
D
70o
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
< MNT = < MTN = 32^\circ
< NMT = 180^\circ - 2(32^\circ) = 116^\circ
< OMN + < NMT + < LMO = 180^\circ
20^\circ + 116^\circ + < LMO = 180^\circ \(\implies\) < LMO = 180^\circ - 136^\circ = 44^\circ
< LMN = < LMO + < OMN
= 44^\circ + 20^\circ = 64^\circ
< NOM = 180^\circ - 2(20^\circ) = 140^\circ
< NLM = \(\frac{1}{2} \times < NOM = 70^\circ\)
< LNM + < LMN + < NLM = 180^\circ
< LNM + 64^\circ + 70^\circ = 180^\circ
< LNM = 180^\circ - 134^\circ = 46^\circ
Source: Myschool Past Questions Archive (Record #26569)