In Fig. 8.139, if AB||CD, then x =
A. 100°
B. 105°
C. 110°
D. 115°
Answers
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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Answer:
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°
Step-by-step explanation:
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