Given,

Ratio of angles of quadrilateral = 3:5:9:13

Let angles are = 3x, 5x, 9x, 13x

So,

3x+5x+9x+13x = 360^∘

30x = 360^∘

Angles would be =

3x = 3×12 = 36

5x = 5×12 = 60^∘

9x = 9×12 = 108^∘

13x = 13×12 = 156^∘