If angle Z is greater than angle X plus angle Y in triangle XYZ, then it must be true that triangle XYZ is an obtuse triangle. An obtuse triangle is a triangle in which one of the angles is greater than 90 degrees. In this case, angle Z must be greater than 90 degrees, which means that triangle XYZ cannot be an acute triangle (where all angles are less than 90 degrees) or a right triangle (where one angle is exactly 90 degrees). Therefore, the only possible option is that triangle XYZ is an obtuse triangle.