Question

In the triangle below, what is the measure of Z?

Answer 1

the X angle will be the same as the Y angle, which is 65

Answer 2

in an isosceles triangle, like the one above, there are two twin sides coming out of a "vertex", in this case the twins are ZX and YX, both coming out of the vertex X.

now, those twin sides make twin angles on the other side, namely the "base", in this case ZY, so if Y is 65°, so is her twin Z.