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

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#### Solution

Let the common ratio between the angles be *x*. Therefore, the angles will be 3*x*, 5*x*, 9*x*, and 13*x*respectively.

As the sum of all interior angles of a quadrilateral is 360º,

∴ 3*x *+ 5*x *+ 9*x *+ 13*x* = 360º

30*x *= 360º

*x *= 12º

Hence, the angles are

3*x* = 3 × 12 = 36º

5*x* = 5 × 12 = 60º

9*x* = 9 × 12 = 108º

13*x* = 13 × 12 = 156º

Concept: Another Condition for a Quadrilateral to Be a Parallelogram

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