Question

If the angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13, then find the measure of the smallest angle.

Answer 1

We have, ∠A : ∠B : ∠C :∠D = 3 : 5 : 9 : 13 .

So, let  ∠A = 3x,

∠B = 5x,

∠C = 9x

and ∠D = 13x

By angle sum property of a quadrilateral, we get:

∠A + ∠B + ∠C + ∠D = 360

  3x + 5x + 9x + 13x = 360

                        30x = 360

                         `x =(360)/(30) `

                         x = 12

Smallest angle is :

∠A = 3x 

∠A = 3(12°)

∠A = 36°

Hence, the smallest angle measures 36°.