How to find the value of $\alpha$ using the attached figure?

Question

I tried to crack this task firstly using constructions like parms and equilateral triangles. This failed since i obtain zero. Also i think in using cosine and sine law but without any important result. As result , is there any helpful way can be used to crack this task.

Answer 1

HINT.

Point $C$ is on the circle with center $A$ and radius $AB$ (because $\angle CBD={1\over2}\angle CAD$).

Hence $\angle BAC=2\alpha$ and $AMCB$ is a cyclic quadrilateral, where $M$ is the point on $AD$.