Below is the original problem. After doing some online research, I came to the conclusion that an actual "SSA" Congruence does not exist, so I was a little confused with what this problem was asking. Anyway, below the picture are my attempts at the answers for the missing parts:

My work so far:

(a) I don't know how these two angles can be supplementary . I did find a corollary that states, "The sum of the measrues of 2 angels of a triangle is less than 180."

(b) XY > YZ

(c) Contradiction to the given that BC ≥ BA.

* I think I got (b) and (c), but part (a) is still throwing me off.

Thank you for your time, help, suggestions/corrections.