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in Lines and Angles by (38.0k points)
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In Fig., if AB || CD, then x =

A. 100°

B. 105°

C. 110°

D. 115°

1 Answer

+1 vote
by (36.4k points)
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Best answer

Given that,

AB ‖ CD

Produce P to Q so that PQ ‖ AB ‖ CD

∠BAP + ∠APQ = 180°(Interior angle)

132° + ∠APQ = 180°

∠APQ = 48° (i)

∠APC = ∠APQ + ∠QPC

148° = 48° + ∠QPC [From (i)]

∠QPC = 100°

∠QPC + ∠PCD = 180°(Interior angles)

100° + ∠PCD = 180°

∠PCD = 80°

∠PCD + x = 180°(Linear pair)

80° + x = 180°

x = 100°

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