The question asks for an angle that is supplementary to $\angle EGF$.

• $\angle EGF$ is the angle formed by the lines $EG$ and $FG$, so this is the angle at point $G$ between the lines $E$ and $F$.
• Two angles are supplementary if their measures add up to 180 degrees.
• From the diagram, we can see that $\angle EGF$ and $\angle BGF$ form a straight line, meaning they are adjacent and supplementary.

Thus, the angle that is supplementary to $\angle EGF$ is $\angle BGF$.

Do you want more details on supplementary angles, or have any other questions? Here are 5 related questions:

1. What is a complementary angle to $\angle EGF$?
2. How do you find vertical angles in this diagram?
3. What is the sum of all angles around point $G$?
4. How do you identify adjacent angles in this diagram?
5. What is the measure of $\angle BGF$ if $\angle EGF$ is 70°?

Tip: Supplementary angles always form a straight line or 180°.