Question

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

Answer 1

let the common multiple be x, a=3x,b=5x,c=9x,d=13x

a+b+c+d=360°( angle sum property of a quadrilateral)

3x+5x+9x+13x=360°

30x=360°

X=360°/30

X=12°

a=3x=3×12°=36°

b=5x=5×12°=60°

c=9x=9×12°=108°

D=13x=13×12°=156°

Answer 2

Let angles in the ratio 3:5:9:13 be a,b,c and d.

Let a=3x,b=5x,c=9x and d=13x.

We know that

Sum of angles of a 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°