1.

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

Answer»

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°



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