Question

1. In Fig. 10.135, if AB || CD, then x =
(a) 100°
(b) 105°
(c) 115°
(d) 110°

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Answer 1

Answer:

Step-by-step explanation:

Given : AB ‖ CD

Construct a line from  P to Q so that PQ ‖ AB ‖ CD

∠BAP + ∠APQ = 180°  

[ Interior angles on the same side of the transversal are supplementary]

132° + ∠APQ = 180°

∠APQ = 180° - 132°

∠APQ = 48°

∠APC = ∠APQ + ∠QPC

148° = 48°  + ∠QPC  

∠QPC = 148° - 48°

∠QPC = 100°

∠QPC + ∠PCD = 180°  

[ Interior angles on the same side of the transversal are supplementary]

100° + ∠PCD = 180°

∠PCD = 180° - 100°

∠PCD = 80°

∠PCD + x = 180°  (Linear pair)

80° + x = 180°

x = 180° - 80°

x = 100°

Hence the value of x is 100°.

Option (A) 100° is correct.

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