The three successive angles of a cycle quadrilateral are in the ratio 1 : 3 : 4, find the measure of the fourth angle ?

Answer: Option A

Sum of the opposite angles in cyclic quadrilateral is 180°
∠A + ∠C = 180°
⇒ x + 4x = 180°
∴ x = 36°
Now ∠B = 3x = 3 × 36° = 108°
∠D = 180 - ∠B = 180 - 108 = 72°