In the given figure, ABCD is a cyclic quadrilateral. Then the ordered pair (x, y) is

A core property of a cyclic quadrilateral states that the sum of opposite interior angles is always equal to $180^{\circ }$.Therefore, the opposite angle pairs satisfy:$\angle A+\angle C=180^{\circ }$$\angle B+\angle D=180^{\circ }$ Let's set up the system of linear equations using the standard UPTET 2017 configuration expressions:$\angle A=4y+20$$\angle B=3y-5$$\angle C=4x$$\angle D=7x+5$ Equation 1:
$$(4y+20)+4x=180$$
$$4x+4y=160⟹x+y=40\text{— (i)}$$
Equation 2:
$$(3y-5)+(7x+5)=180$$
$$7x+3y=180\text{— (ii)}$$
Now, solve the simultaneous equations. From equation (i), express $y$ in terms of $x$:
$$y=40-x$$
Substitute this value of $y$ into equation (ii):
$$7x+3(40-x)=180$$
$$7x+120-3x=180$$
$$4x=60⟹x=15^{\circ }$$
Substitute $x=15^{\circ }$ back into the expression for $y$:
$$y=40-15=25^{\circ }$$
Thus, the ordered pair solution $(x,y)$ is $(15^{\circ },25^{\circ })$.