The angles of a quadrilateral are in the ratio 3:5:9:13.

Question:
The angles of a quadrilateral are in the ratio 3:5:9:13. Find all the angles of the quadrilateral.

Solution:

Let the common ratio between the angles is 't'

So the angles will be 3t, 5t, 9t and 13t respectively.

Since the sum of all interior angles of a quadrilateral is 360^°

Therefore, 3t + 5t + 9t + 13t = 360^°

⟹ 30t = 360^°

⟹ t = 12^°

Hence, the angles are

3t = 3*12 = 36^°

5t = 5*12 = 60^°

9t = 9*12 = 108^°

13t = 13*12 = 156^°