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To find which angle is supplementary to \(\angle EFG\), we need to identify the angle in question on the diagram and find the angle that, when added to \(\angle EFG\), equals \(180^\circ\).

### Analysis:
- \(\angle EFG\) is the angle formed at point \(F\) between lines \(EF\) and \(FG\).
- An angle is supplementary to \(\angle EFG\) if the two angles add up to \(180^\circ\).
- In the diagram, \(\angle EFI\) is directly adjacent to \(\angle EFG\) along the same straight line, making these two angles supplementary because they form a straight line together.

### Conclusion:
The angle that is supplementary to \(\angle EFG\) is \(\angle EFI\).

Would you like more details or have any other questions?

### Related Questions:
1. What is the definition of supplementary angles?
2. How do you identify adjacent angles in a diagram?
3. Can two angles be supplementary if they are not adjacent?
4. How do you calculate unknown supplementary angles?
5. What is the difference between complementary and supplementary angles?

### Tip:
To determine supplementary angles, always look for pairs of angles that form a straight line or add up to \(180^\circ\).

In this geometry problem, students are asked to determine which angle is supplementary to ∠EFG based on a provided diagram. Supplementary angles are defined as two angles that sum to 180°. This solution explains how to identify adjacent angles that form a straight line.

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