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

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

Given the ratio between the angles of the quadrilateral = 3 : 5 : 9 : 13 and 3 + 5 + 9 + 13 = 30 

Since, the sum of the angles of the quadrilateral = 360⁰ 

∴ First angle of it = 3/30 × 360⁰ = 36⁰ , 

 Second angle = 5/30 × 360⁰ = 60⁰ , 

 Third angle = 9/30 × 360⁰ = 108⁰ , 

 And, Fourth angle = 13/30 × 360⁰ = 156⁰ 

∴ The angles of quadrilateral are 360⁰ , 60⁰ , 108⁰ and 156⁰ . 

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

Let ∠A+ ∠B : ∠C : ∠D = 3 : 5 : 9 : 13. 

Sum of ratio = 3x + 5x + 9x + 13x = 30x 

Sum of 4 angles of quadrilateral is 360° 

∴ ∠A + ∠B + ∠C + ∠D = 360° 

3x + 5x + 9x + 13x = 360 

30x = 360 ∴ x = = 12° 

∠A = 3x = 3 × 12 = 36° 

∠B = 5x = 5 × 12 = 60° 

∠C = 9x = 9 × 12 = 108° 

∠D = 13x = 13 × 12 = 156°