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+1 vote
6.1k views
in Mathematics by (30.0k points)

In the figure, if AB || CD, ∠APQ = 50° and ∠PRD = 127°, find x and y.

1 Answer

+1 vote
by (130k points)
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In the given figure, AB || CD, ∠APQ = 50° 

and ∠PRD = 127° 

∠APQ + ∠PQC = 180° 

[Pair of consecutive interior angles are supplementary] 

⇒ 50° + ∠PQC = 180° 

⇒ ∠PQC = 180° – 50° = 130° 

Now, ∠PQC + ∠PQR = 180° [Linear pair axiom] 

⇒ 130° + x = 180° 

⇒ x = 180° – 130° = 50° 

Also, x + y = 127° 

[Exterior angle of a triangle is equal to the sum of the two interior opposite angles] 

⇒ 50° + y = 127° 

⇒ y = 127° – 50° = 77° 

Hence, x = 50° and y = 77° Ans.

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