It is 45 deg. = π/4.
Since, XYZ is a right angle triangle at Y, angle Y = π/2.
Since it is an isosceles triangle: angle X = angle Z
sum of angles X + angle Z = π - angle Y = π - π/2 = π/2
hence angle X = angle Z = π/4
Now, the triangle XNM is also an isosceles right angle triangle. The reasons:
1. NM is a line joining the mid points of sides XY and XZ respectively. Hence NM is parallel to the third side YZ. also, the length of NM is 1/2 * YZ
2. As NM || YZ, the transversal XZ cuts the two parallel lines at Z and N. The angles XZY and XNM are equal. They are included angles on the same side of transversal. Hence, angle XNM = angle XZY = π/4.
3. As NM || YZ and YZ is perpendicular to XY, NM is perpendicular to XY. Hence angle at N in triangle XNM is also a right angle.