In the given figure AB || CD. MT = MO, m∠RTD = 48°. m∠PNB = 3x then, what is the value of x?
32°
Since O, T, R are collinear and C, M, T, D are collinear, ∠MTO and ∠RTD are vertically opposite angles, so ∠MTO = 48°.
Since MT = MO, triangle MOT is isosceles, so ∠MOT = ∠MTO = 48°. Hence ∠OMT = 180 - 48 - 48 = 84°.
Since O, M, N, P are collinear, ∠NMD = 180 - 84 = 96° (linear pair on line CD at M).
Since AB ∥ CD with transversal O-M-N-P, ∠PNB and ∠NMD are corresponding angles, so ∠PNB = 96°.
3x = 96 ⇒ x = 32°. Answer: (C).
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