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To determine which angles are adjacent in the given diagram, we need to identify angles that share a common side and a common vertex, without overlapping.

- \( \angle DCF \) shares the vertex \( C \) with other angles.
- From the diagram, \( \angle DCF \) and \( \angle GFC \) are adjacent because they both share the vertex \( C \) and the side \( CF \) (the line between points \( C \) and \( F \)), and they do not overlap.

Thus, the correct answer is **\( \angle DCF \) and \( \angle GFC \)**.

Would you like further clarification or details on adjacent angles?

Here are 5 related questions:
1. What is the definition of adjacent angles in geometry?
2. Can adjacent angles be supplementary? If so, under what conditions?
3. How can you determine if two angles are adjacent in complex figures?
4. What are the properties of vertical angles, and how do they relate to adjacent angles?
5. How do adjacent angles differ from complementary or supplementary angles?

**Tip**: Adjacent angles always share a common vertex and one common side, but they do not overlap.

Learn how to identify adjacent angles in a geometric figure. Understand the key concepts of adjacent angles, including the conditions required for angles to be adjacent. Suitable for students in Grades 6-8.

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