Problem

Workings

I was able to show that the triangles ABD & ACD are congruent as $AD$ is a common side and as $\angle BAC $ is bisected & $\angle ABC = \angle ACB$ give which makes them congruent by Angle Angle Side.

Where do I need help:

I am having trouble showing,

Show that $\angle XYA = \angle BXE$

& $\angle BEX = \angle BXE + \angle EBX$