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The question asks which of the given rotations will map the polygon onto itself. The polygon shown is a square, as indicated by its four equal sides and right angles.

For a square, rotations that map it onto itself (known as symmetries) must be multiples of \(90^\circ\) because it has four symmetrical positions (0°, 90°, 180°, and 270°).

Let's examine each option:

1. **Rotation of 45° clockwise**: This does not map the square onto itself, as 45° is not a multiple of 90°.
2. **Rotation of 90° counterclockwise**: This does map the square onto itself because 90° is one of the symmetrical rotations.
3. **Rotation of 120° counterclockwise**: This does not map the square onto itself, as 120° is not a multiple of 90°.
4. **Rotation of 30° counterclockwise**: This does not map the square onto itself, as 30° is not a multiple of 90°.

So, only the **90° rotation** (option 2) will carry the square onto itself. 

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

Here are some additional related questions to explore:

1. What are the rotational symmetries of other regular polygons, like a hexagon?
2. How can we identify the angle of rotation symmetry for any regular polygon?
3. What other types of transformations can map a square onto itself?
4. What is the relationship between the number of sides of a regular polygon and its angle of rotation symmetry?
5. How do rotational and reflectional symmetries differ in polygons?

**Tip:** For a regular polygon with \( n \) sides, the smallest angle of rotation symmetry is \( \frac{360^\circ}{n} \).

Which of the following transformations carry this regular polygon onto itself? (The polygon is a square.)

Explore which rotations carry a square onto itself. Learn about rotational symmetry and the conditions for a square to map onto itself. Suitable for Grades 7-9 students studying geometry.

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