## Elementary Geometry for College Students (7th Edition)

1. Z is the midpoint of XW, so by definition, XZ is congruent to ZW. 2. We are told that XZ is congruent to YZ, so YZ is congruent to ZW. 3. Thus, both XYZ and YZW are isosceles, meaning e = a and f = d. 4. Thus, we obtain that: $2e + b = 180$ And $2f + 180 - b = 180$ Adding these gives: $2(e+f) = 180 \\ e+ f = 90$ Thus, since XYZ equals e plus f, XYZ is 90 degrees.