Question

The angles of Quadrilateral are In ratio 3 : 5 : 9 : 13 . Find All the Angles! ​

Answer 1

Step-by-step explanation:

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°

Answer 2

Answer:

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

let a = 3x, b= 5x, C = 9x, d = 13x

where x is any number..

we know that

sum of angles of quadrilateral is 360°

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

3x + 5x + 9x + 13x = 360°

30x = 360°

x = 360°/ 30

x = 12°

hence the angles are..

a = 3x = 3 x 12° = 36°

b = 5x = 5 x 12° = 60°

c = 9x = 9 x 12° = 108°

d = 13x = 13 x 12° = 156°

hope it's helps you...