Question

In a quadrilateral the angles are in the ratio $2:4:5:7$ then find the difference between the greatest and the smallest angle.

Answer 1

Sum of a angle of a quadrilateral $=360°$

The ratio of angles $=2:4:5:7$

let the angles be $2x,4x,5x,7x$.

So, $2x+4x+5x+7x=360°18x=360°x=20°$

So, $1^{st}$ angle $=2x=40°$

$2^{nd}$ angle $=4x=80°$

$3^{rd}$ angle $=5x=100°$

$4^{th}$ angle $=7x=140°$

Hence, difference between the greatest and smallest angle = ${140}^o-{40}^o={100}^o$