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Answer :

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 = \(-7x + 5 = -7(-15) + 5 = 110°\)

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