Find the value of $x\text{ and }y$  if  $ABCD$ is cyclic quadrilateral.

Concept: Every angle of a cyclic quadrilateral is on a circle (circumscribed circle), and the sum of any two opposite angles of a cyclic quadrilateral is 180˚.

Here, $ABCD$is a cyclic quadrilateral.

Then, sum of any pair of opposite angles of cyclic quadrilateral is ${180}^0$ .

From figure,  $\angle BAD+\angle BCD={180}^{°}\Rightarrow x+2y={180}^{°} ..\left(i\right)$AND 

$\angle ADC+\angle CBA={180}^{°}\Rightarrow (x+y)+(2x-y)={180}^{°} ......\left(2\right)$When solving equation (i) and (ii), we get

$x={60}^{°}\&y={60}^{°}$

Hence, $x={60}^{°}\&y={60}^{°}$