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To solve this question, we need to identify which angles are supplementary to \( \angle EGF \). 

Supplementary angles add up to \( 180^\circ \). From the diagram, \( \angle EGF \) is formed by the rays \( GE \) and \( GF \), and we must find all angles that, when added to \( \angle EGF \), form a straight line (i.e., sum to \( 180^\circ \)).

Looking at the diagram:

- \( \angle EGF \) forms a straight line with \( \angle FGB \), as they are adjacent and together form a straight line.
- Similarly, \( \angle EGF \) is supplementary to \( \angle DGF \), because \( GD \) and \( GE \) form another straight line through \( G \).
- \( \angle EGF \) is supplementary to \( \angle CGE \), as they are adjacent and together form a straight angle along the line passing through points \( C, G, E \).
  
The other options, such as \( \angle AGC \) and \( \angle DGF \), may not directly form supplementary pairs with \( \angle EGF \).

### Correct options for supplementary angles to \( \angle EGF \):
- \( \angle FGB \)
- \( \angle DGF \)
- \( \angle CGE \)

Would you like a more detailed explanation or have any other questions?

### Related Questions:
1. What is the definition of supplementary angles?
2. How do we determine whether two angles are supplementary in a diagram like this?
3. Can two adjacent angles not be supplementary? Why?
4. What are adjacent angles, and how do they relate to supplementary angles?
5. How does the concept of a straight line help in identifying supplementary angles?

### Tip:
Always check if two angles share a common ray and form a straight line when identifying supplementary angles in a diagram.

Which angles are supplementary to ∠EGF? Select all that apply.

Learn how to determine which angles are supplementary to ∠EGF in a geometry diagram. This problem involves identifying angles that form a straight line and add up to 180 degrees. Perfect for students in Grades 6-8 studying geometry concepts like supplementary and linear pairs.

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