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

Given : ∠APQ = 50° and ∠PRD = 127°.

From figure,

PQ is the transversal.

⇒ ∠PQR = ∠APQ (Alternate interior angles are equal)

⇒ x = 50°.

From figure,

⇒ ∠PRQ + ∠PRD = 180° [Linear pairs]

⇒ ∠PRQ + 127° = 180°

⇒ ∠PRQ = 180° - 127° = 53°.

By angle sum property of triangle :

⇒ ∠PQR + ∠QPR + ∠PRQ = 180°

⇒ x + y + 53° = 180°

⇒ 50° + y + 53° = 180°

⇒ y = 180° - 103°

⇒ y = 77°

Hence, x = 50° and y = 77°.