It's not clear where point Y is located. If Y is the midpoint, and Y is on line XZ, then we can say that XY = 25 and YZ = 25 (since Y cuts XZ in half; the two equal portions are XY and YZ)
I'm using the segment addition postulate XY+YZ = XZ
However, all of this is based on the assumption that Y is the midpoint and on line XZ.