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Find the value of x and y if ABCD is a cyclic quadrilateral.

We know that the sum of either pair of opposite angles of a cyclic quadrilateral is 180^o.

So in cyclic quadrilateral ABCD,

∠D + ∠B = 180^o

⇒ (x + y) + (2x - y) = 180^o

⇒ 3x = 180^o

⇒ x = 60^o

Similarly,

∠A + ∠C = 180^o

⇒ x + 2y = 180^o

⇒ 60^o + 2y = 180^o

⇒ 2y = 120^o

⇒ y = 60^o

Hence, x = 60^o and y = 60^o