Attachment:

Triangle.PNG

In the triangle above, what is the length of the side BC?

(1) Line segment AD has length 6

(2) x= 36

Can someone please explain the logic behind the explanation given in

the official guide for the quantitative review-1st edition (question #117).

What I can't understand from the explanation is that it has been assumed that

angle ABD + angle DAB = 2x

will imply that ABD = DAB =x.

Why is the above true? Isn't it possible that ABD = 1.5x and DAB = 0.5x?

Why those two have to be equal?