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 180⁰.

Therefore,

∠A + ∠C = 180⁰

4y + 20 - 4x = 180 - 4x + 4y = 160

x - y = - 40 (i)

Also,

∠B + ∠D = 180⁰

3y - 5 - 7x + 5 = 180 - 7x + 3y = 180 (ii)

Multiplying equation (1) by 3, we obtain:
3x - 3y = - 120 (iii)

Adding equations (2) and (3), we obtain:
- 7x + 3x = 180 - 120
- 4x = 60
x = -15

By using equation (i), we obtain x - y = - 40
-15 - y = - 40
y = -15 + 40 = 25

∠A = 4y + 20⁰  = 4(25) + 20⁰ = 120⁰

∠B = 3y - 5 = 3(25) -5 = 70⁰

∠C = -4x = -4 (-15) = 60⁰