Answer:
60°
Step-by-step explanation:
Triangle XYZ is equilateral triangle. In equilateral triangle all interior angles have measures of 60° each.
Line XM is perpendicular to the side YZ. Then this line is also an angle X bisector (the height of the equilateral triangle is also its median and angle bisector), so
m∠MXN = 30°
Consider triangle MNX. This is right triangle, because MN ⊥ XZ.
The sum of the measures of all interior angles in the triangle is always 180°, so
[tex]m\angle MXN+m\angle MNX+m\angle NMX=180^{\circ}\\ \\30^{\circ}+90^{\circ}+m\angle NMX=180^{\circ}\\ \\m\angle NMX=180^{\circ}-30^{\circ}-90^{\circ}=60^{\circ}[/tex]
