In a cyclic quadrilateral ABCD , . Find the four angles.

Opposite angles of a cyclic quadrilateral are supplementary

∠A + ∠C = 180°

∠B + ∠D = 180°

Given, ,

2x + 4 + 2y + 10 = 180

⇒ x + y = 83 ------- (1)

y + 3 + 4x – 5 = 180

⇒ y + 4x = 182 -------- (2)

(1) – (2)

⇒ x – 4x = 83 – 182

⇒ x = 33

Thus, y = 50

∠A = 2x + 4 = 70°

∠B = y + 3 = 53°

∠C = 2y + 10 = 110°

∠D = 4x – 5 = 127°