If triangle ZXY is an equilateral triangle and the measure of W equals 34 degrees, what is the measure of the triangle WXZ?

Question

Work: XZ bisects WXZ and ZXY ; since W is 34 degrees, than Y is 34 degrees and since ZXY is equilateral, that also means that Z is 34 degrees.

Answer 1

Can't quite fathom your terminology.
How do you take the measure of a triangle? I'll assume that WXZ is an angle, not a triangle.

If XZ is a side of the triangle ZXY, how can it bisect ZXY?

I'll assume your logic is sound, even if your exposition is not.