Can someone me with this question ?

<BAX = <ADY
AB || CD                    Property of a square.
<BAX = Theta           Naming an angle (doesn't need proof)
<BAX = <AZD           Property of parallel lines
<ZDY = 90 - Theta    Right angle triangle
<YDA = theta            The two angles at D are complementary.
Which was what you were intended to prove.

Triangle DAY and ABX are Congruent.
You know this because you have two angles and a side that are equal. If two angles in a triangle are equal then the third angle is equal. You have AAS but you could easily make it into ASA. The key step is the one above.

Nice problem. Thanks for posting.