The two angles of a quadrangle are 4: 5. The third angle is the sum of the two angles

The two angles of a quadrangle are 4: 5. The third angle is the sum of the two angles and the fourth is 90 degrees. Find the corner of this quadrilateral

Let’s denote the corners of the quadrangle as a, b, c, d.

Then (a + b + c + d) = 360.

By assumption, d = 90, c = (a + b), a / b = 4/5.

(a + b + (a + b) + 90) = 36.

2 * a + 2 * b = 360 – 90 = 27.

a + b = 135.

a = 135 – b.

a = (4/5) * b.

135 – b = (4/5) * b.

135 = (4/5) * b + b = (9/5) * b.

b = (135 * 5) / 9 = 75.

a = (4/5) * 75 = 60.

c = 75 + 60 = 135.

d = 90.

Answer: The angles of the quadrangle are 60, 75, 135, 90 degrees.