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°