If the interior angles of a quadrilateral are in the ratio 1:2:3:4, prove that it is a cyclic quadrilateral.

Given : The angles of quadrilateral ABCD are in the ratio 1 : 2 : 3 : 4.

Let the angles of quadrilateral ABCD be x, 2x, 3x and 4x respectively.

As, we know that the sum of angles of quadrilateral is 360°

⇒ ∠A = 36°, ∠B = 2 × 36° = 72°, ∠C = 3 × 36° = 108° and ∠D = 4 × 36° = 144°
Now you can see that
∠A +∠C = ∠B +∠D = 180 so quadrilateral is a cyclic quadrilateral