ABCD is a cyclic quadrilateral. Find the angles of the cyclic quadrilateral.

It is given a cyclic quadrilateral whose angles are given in variable. So, it need to be found.

The sum of opposite angles in a quadrilateral is 180^o.

So,

∠A + ∠C = 180

⇒ ( 4y + 20) + ( -4x) = 180

⇒ 4y – 4x = 160

Y = 160 + 4x / 4 = 40 + x …(i)

and

∠B + ∠D = 180

⇒ ( 3y - 5) + (-7x + 5) = 180

⇒ 3y – 7x = 180

Putting the value of equation (i),

The angles of the cyclic quadrilateral are 120^o, 70 ^o, 60 ^o, 110 ^o