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°

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