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

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Suppose the measures of four angles are 3x, 5x, 9x and 13x. 

∴ 3x + 5x + 9x + 13x = 360° [Angle sum property of a quadrilateral] 

⇒ 30x = 360° 

⇒ x = 360/ 30 ° = 12° 

⇒ 3x = 3 × 12° = 36° 

5x = 5 × 12° = 60° 

9x = 9 × 12° = 108° 

13x = 13 × 12° = 156° 

∴ the angles of the quadrilateral are 36°, 60°, 108° and 156° Ans

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