arpitalewe wrote:

In this why can't we take angle ADB = 120 degrees which can provide angle DAB = 15 degrees and since BD = 1/2 CD so DAC = 30 degrees.

What's wrong in this approach?

This is wrong. The property you are referring works for angles and sides within a triangle but here you are comparing two different triangles. However you can use the angle bisector theorem here, according to which:

\(CD/DB = sin(angle DAC)/sin (angle DAB)\)

Now you need to know the value of sin15 and find the double of it and then find the angle whose value is represented by that sin value. Here is the link from wiki for angle bisector theorem:

https://en.wikipedia.org/wiki/Angle_bisector_theorem
_________________

Retaking gmat for second time, any re-takers please feel free to connect.