Question

The difference between the smallest and second smallest angles of a quadrilateral is equal to the difference between the biggest and second biggest angles. If the biggest angle is twice the smallest angle, what is the measure of the smallest angle?

(Solution pls... Tnx)

Answer 1

let the angles in order of size be
x , a , b, 2x

"The difference between the smallest and second smallest angles" ---> a-x
"the difference between the biggest and second biggest angles" ---> 2x-b

2x - b = a - x
3x = a+b

also we know
x + a + b + 2x = 360
x + 3x + 2x = 360
6x = 360
x = 60
The smallest ist 60° and the largest is 120°

We were lucky that a+b could be expressed in terms of x