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