In the figure (ii) given below, O is the center of the circle. If ∠OAD = 50°, find the values of x and y.

From figure,

ABCD is a cyclic quadrilateral as all vertices lie on the circumference of the circle.

Sum of opposite angles of cyclic quadrilateral = 180°

⇒ ∠BCD + ∠BAD = 180°
⇒ x + 50° = 180°
⇒ x = 180° - 50°
⇒ x = 130°.

OA = OD = radius of the circle.

So, in △ODA,

∠ODA = ∠OAD = 50°.

In triangle exterior angle is equal to the sum of the opposite two interior angle.

y = ∠ODA + ∠OAD = 50° + 50° = 100°.

Hence, the value of x = 130° and y = 100°.