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.
44o
46o
52o
70o
Correct answer is B
< MNT = < MTN = 32°
< NMT = 180° - 2(32°) = 116°
< OMN + < NMT + < LMO = 180°
20° + 116° + < LMO = 180° ⟹ < 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°
Similar Questions
For what range of values of x is \frac{1}{2}x + \frac{1}{4} > \frac{1}{3}x + \(\frac{...
If the exterior angles of a pentagon are x°, (x + 5)°, (x + 10)°, (x + 15)° and...
Find the median of 2, 1, 0, 3, 1, 1, 4, 0, 1 and 2 ...
The graph of y = x^2 and y = x intersect at which of these points?...
An arc subtends an angle of 30<sup>o</sup> at the centre of a circle radius 12cm. Calcul...
If cos θ = 5/13, what is the value of tan \theta for 0 < θ < 90°...
Find the area and perimeter of a square whose length of diagonals is 20\sqrt2 cm...