I think there's an incorrect question, please correct me if that is not the case!

GRE Quant Problem Solving
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Is this not incorrect? As per Greg, the answer to this is D. Because ASS cannot be used to prove that the two triangles are identical. And as per the explanation only Z is the common angle.

However, the question also shows the two triangles having two identical sides x and y. For x to be identical, angle Z is identical (given). Now, for y to also be identical the opposite angle will have to be the same too.

In which case we have two identical angles (by consequence the third one will be too) - is that not sufficient for the answer to be C?

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Consider this example:

Let z = 30^{\circ} and x = 3.

If \angle C = 60^{\circ}, we get that y = 3 \sqrt{3}. Similarly, if \angle C = (180 - 60)^{\circ}, we still get y = 3 \sqrt{3}.

Thus, \angle C is certainly not fixed as you claimed.