ABCD is a cyclic quadrilateral (see figure). Find the angles of the cyclic quadrilateral.

We know that the sum of the measures of opposite angles in a cyclic quadrilateral is :

\( \angle \)A + \( \angle \)C = 180°
=>\(4y + 20 - 4x = 180°\)
=>\(-4x + 4y = 160°\)
=>\(x - y = -40°\) ………(1)
Also \( \angle \)B + \( \angle \)D = 180°
=>\(3y - 5 - 7x + 5 = 180°\)
=>\(-7x + 3y = 180°\)………(2)

Multiplying equation (1) by 3:
\(3x - 3y = - 120°\) ……….(3)

Adding equations (2) and (3):
\(-4x = 60° => x = -15°\)

Substituting the value of in equation (1):
\(-15 - y = -40°\)
=>\(y = -15 + 40 =25\)
\( \angle \)A = \(4y + 20 = 4(25) + 20 = 120°\)
\( \angle \)B = \(3y - 5 = 3(25) - 5 = 70°\)
\( \angle \)C = \(-4x = -4(-15) = 60°\)
\( \angle \)D = \(-7x + 5 = -7(-15) + 5 = 110°\)