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To find the angle that is supplementary to ∠DCF in the given diagram, let's analyze the options and the diagram. Supplementary angles are pairs of angles that add up to 180°.

### Analysis:
- ∠DCF is the angle formed between line segments DC and CF.
- For an angle to be supplementary to ∠DCF, it needs to be adjacent to it and form a straight line, which will add up to 180°.

### Identifying the Supplementary Angle:
- In the diagram, ∠DCF is adjacent to ∠FCD, and together they form a straight line along line DF.
- Therefore, ∠FCD is the angle that is supplementary to ∠DCF.

### Correct Answer:
**∠FCD** is supplementary to ∠DCF.

Would you like further details or have any other questions?

Here are 5 related questions:
1. What are complementary angles, and how do they differ from supplementary angles?
2. How can you determine if two angles are adjacent?
3. What is the definition of a linear pair of angles?
4. If ∠DCF measures 70°, what would be the measure of its supplementary angle?
5. How do you find the angle between intersecting lines?

**Tip:** Remember, supplementary angles always add up to 180°, so if you know one angle, you can find the other by subtracting it from 180°.

Which angle is supplementary to the ∠DCF in this diagram?

Learn how to identify which angle is supplementary to ∠DCF in a given geometric diagram. This problem focuses on the concept of supplementary angles, adjacent angles, and the Linear Pair Theorem. Ideal for students in Grades 7-10 seeking to understand angle relationships.

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