We can see from the diagram (in the comments) that ∠UWV and ∠XWZ are vertical angles; this is because they are opposite angles that share only a vertex.
We can also see that both of these angles are 90°.
This gives us two angle measures of triangle WXZ, 50 and 90. We know that the sum of the measures of the angles of a triangle is 180°; this gives us
So you know that the sum of angles in a triangle is 180°. You know two of the angles in triangle WXZ. The two angles are angle WXZ, which is 50° and angle XWZ, which is 90°.
Now you can calculate angle WZX, by: 180-50-90=40°.