in a quadrilateral ABCD, angle A +angle C is 2 times angle B + angle D. if angle A = 40 degree,then angle B =

Let us observe the following figure.

Given that,

.....(1)

Also given that 

We know that in a quadrilateral,

.....(2)

We need to find the angle B.

Substitute in equations(1) and (2) respectively, we have

.....(3)

......(4)

Adding equations(3) and (4) we have, 

......(5)

Subtract equation (5) from equation f(4), we have

Substitute the values and in equation (1) we have

Thus,

Therefore we need to have one more condition to get the unique solution of or the vaule of is such that