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.
