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The question is asking which transformations will carry this regular hexagon onto itself. For a regular hexagon, there are several transformations that can map it back onto itself, including specific rotations and reflections.

### Explanation of each option:
1. **Rotation of 72° clockwise**: Since 72° is not a multiple of 60°, it would not map a regular hexagon onto itself, as the angles between each side of a regular hexagon are 60°.
   
2. **Rotation of 60° clockwise**: This is valid. A rotation of 60° (or any multiple of 60°) will map the hexagon onto itself since it has six-fold rotational symmetry.

3. **Reflection across line \( l \)**: If line \( l \) is an axis of symmetry through opposite vertices or midpoints of opposite sides, then a reflection across this line would map the hexagon onto itself.

4. **Rotation of 60° counterclockwise**: This is also valid for the same reason as option 2; rotating by 60° counterclockwise will map the hexagon onto itself.

### Correct Answers:
The transformations that map the hexagon onto itself are:
- **Rotation of 60° clockwise**
- **Reflection across line \( l \)** (assuming line \( l \) is a symmetry axis)
- **Rotation of 60° counterclockwise**

Let me know if you need further details or explanations!

### Related Questions:
1. What are the symmetries of a regular hexagon?
2. How do rotational symmetries differ between polygons with different numbers of sides?
3. Why does a regular hexagon have six axes of symmetry?
4. What other transformations map regular polygons onto themselves?
5. How can you determine rotational symmetry for any regular polygon?

### Tip:
To find rotational symmetries of a regular polygon, divide 360° by the number of sides to find the smallest rotation angle that maps the shape onto itself.

Which of the following transformations carry this regular polygon onto itself?

Explore the transformations that can map a regular hexagon onto itself, including rotations and reflections. This problem covers key geometric concepts such as rotational and reflection symmetry, suitable for students in Grades 8-10.

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