In Fig., if AB || CD, then x =A. 100°B. 105°C. 110°D. 115°

1.	In Fig., if AB \|\| CD, then x =A. 100°B. 105°C. 110°D. 115°
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°

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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