Question

The image shown has two triangles sharing a vertex:

Answer 1

Answer:

40°.

Step-by-step explanation:

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

180-(50+90) = 180-140 = 40° for the angle.

Answer 2

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°.