Question 311309
Every quadrilateral in a plane contains a total of 360 degrees.
If the ratio of the interior angles is 4:9:5:6, we can set them equal to
4x, 9x, 5x and 6x, and then set their sum equal to 360 degrees.

Thus 4x + 9x + 5x + 6x = 360
24x = 360
x = 15 
and the angles are then
60, 135, 75, and 90 degrees, respectively.