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°.