To solve this question, we need to find which angle is supplementary to $\angle EFG$. Two angles are supplementary if the sum of their measures equals 180 degrees.

In the diagram, $\angle EFG$ is formed by the points $E$, $F$, and $G$, and we observe that the line segment $FG$ is a part of the straight line $HFG$.

This means the angle supplementary to $\angle EFG$ must share the same vertex $F$ and form a linear pair with $\angle EFG$. In this case, the angle on the other side of $\angle EFG$, along the straight line $HFG$, is $\angle GFH$, which lies along the same line and would add up with $\angle EFG$ to 180°.

Thus, the correct answer is $\angle GFH$.

Would you like further clarification or details on the reasoning? Here are some related questions for further exploration:

1. What is the definition of supplementary angles?
2. Can two right angles be supplementary?
3. How do you identify linear pairs in geometric figures?
4. Are complementary angles always adjacent?
5. How are adjacent angles and supplementary angles related?

Tip: Remember that supplementary angles don't have to be adjacent; their sum just needs to be 180 degrees!