Question

The angles of a quadrilateral are in the ratio 3:5:9:13, then the measure of the largest angle is ----

Answer 1

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°