The angles A, B, C of the quadrilateral ABCD are related as 1: 2: 4. Find the angle D

The angles A, B, C of the quadrilateral ABCD are related as 1: 2: 4. Find the angle D if a circle can be described around this quadrilateral.

If a circle can be described around a quadrilateral, then this quadrilateral is convex and the sum of its opposite sides is 180.

A + C = 180.

B + D = 180.

Let’s take one part of the ratio of the angles as X, then A = 1 * X, B = 2 * X, C = 4 * X.

A + C = 180.

1 * X + 4 * X = 180.

X = 180/5 = 360.

Then:

B + D = 180.

2 * 36 + D = 180.

D = 180 -72 = 108.

Answer: Angle D = 108.