OA = OB [Radius]

∴ ∠OAB = ∠OBC = 50°

In triangle AOB,

∠AOB + ∠OAB + ∠OBC = 180°[Sum of angles of triangle]

⇒ ∠AOB + 50° + 50° = 180°

⇒ ∠AOB + 100° = 180°

⇒ ∠AOB = 80°

∴ x = 180°– ∠AOB [AOD is a straight line]

⇒ x = 180°- 80°

⇒ x = 100°

∴ X + Y = 180°[Opposite angle of a cyclic quadrilateral are supplementary]

⇒ 100° + Y = 180°

⇒ Y = 80°