Triangle abc is similar to triangle def. what is the measure of angle def? refer to image, show work : )

Remember, all the interior angles of a triangle equals 180.
So in triangle ABC, it already gives us two out of the three angles. 

First, we add 52 and 36 and that gives us 88.

Now we subtract 88 from 180.

180 - 88 = 92

So that means that ∠ABC is 92°

Now we have to look at triangle DEF. 
The equation says that triangle DEF is similar to triangle ABC.

Looking at the picture, triangle DEF is smaller and is flipped upside down.

So that means that ∠ABC ≈ ∠DEF

In similar triangles, the measurements of angles does NOT change. Just the side length.

So since ∠ABC = 92° that means that ∠DEF = 92°