Answer: Choice A
Angle EIG = Angle FIH; Angle EIF = Angle GIH
---------------------------------------------------------------------------
Note the square angle markers. They tell the reader "this angle is 90 degrees". So we see that angle EIG and angle FIH are each 90 degrees; therefore, they are congruent (aka equal) angles. This narrows the answer between choice A or choice B.
Let's say that angle EIF is x degrees. This would make angle FIG to be 90-x because EIF and FIG must add to 90. Let angle GIH be y degrees. This means that FIG is 90-y degrees (for similar reasons as before). So angle FIG is both 90-x and 90-y forcing x = y to be true. Ultimately, this means that angle EIF and angle GIH are the same measure. So that's why the final answer is choice A.
