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To solve the problem, we need to find an angle that is supplementary to \(\angle EGF\). 

### Supplementary Angles Definition:
Two angles are called supplementary if their measures add up to 180 degrees.

### Analysis of \(\angle EGF\):
- In the diagram, \(\angle EGF\) is formed by the rays \(GE\) and \(GF\).
- We need to identify the angle that, when added to \(\angle EGF\), equals 180°.

Since \(EGF\) is part of a straight line, the supplementary angle must share the same vertex \(G\) and lie on the opposite side of the angle formed by \(EG\) and \(GF\).

### Observation:
The ray opposite to \(GF\) is \(GA\), and the ray opposite to \(GE\) is \(GD\). Therefore, the angle formed by these rays on the other side of \(EGF\) is \(\angle AGD\).

### Conclusion:
The angle that is supplementary to \(\angle EGF\) is \(\angle AGD\).

Would you like further details on the supplementary angle property or the reasoning process? 

Here are five related questions:
1. What are complementary angles?
2. How can we find angles that are vertical to each other?
3. Can an angle be supplementary to itself? Why or why not?
4. How do we define adjacent angles?
5. What is the relationship between linear pairs of angles?

**Tip:** When dealing with straight angles, always look for the opposite rays, as they help identify supplementary angles easily.

What is an angle that is supplementary to ∠EGF?

Explore how to determine the angle supplementary to ∠EGF using the concept of supplementary angles. This geometry problem demonstrates how two angles that add up to 180° can be found in a diagram, suitable for Grades 6-8.

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