The image shown has two triangles sharing a vertex:
what is the measure of ∠wzx, and why?

a. y over 2, because triangle uvw is congruent to triangle wxz
b. y, because triangle uvw is similar to triangle zxw
c. y + 50 degrees, because triangle uvw is similar to triangle zxw
d. 130 degrees − y, because triangle uvw is congruent to triangle wxz

The answer is B. Angles UVW ad ZXW are congruent, and because of the vertical angle theorem, angles UWV and XWZ are congruent. So if 2 angles in each triangle are congruent to each other, then the triangle angle sum theorem tells us that the third angle also has to be congruent in each.  BUT congruent angles do not make the triangles congruent because the length of the sides can change and the measures of the angles remain unchanged. Therefore, the triangles can only be said to be similar (if the lengths of the sides were given we could determine whether they were actually congruent, but they're not so we don't know for sure if they are congruent, only that they are similar). So B.

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