The problem involves identifying all the degrees of rotation that carry a square back onto itself when rotated clockwise about its center point $P$.

Key Concept:

A square exhibits rotational symmetry of order 4. This means the square looks identical after being rotated by multiples of $90^\circ$.

Correct Rotations:

The square will align perfectly onto itself at these rotations:

• $90^\circ$
• $180^\circ$
• $270^\circ$
• $360^\circ$ (a full rotation)

These degrees of rotation are the correct answers.

Would you like a detailed explanation of rotational symmetry? Let me know if you have any questions or need further clarifications!

Follow-up Questions:

1. What is the difference between rotational and reflectional symmetry?
2. How does the symmetry order change for other regular polygons?
3. Why is $45^\circ$ not a valid rotation for a square?
4. Can rotational symmetry be applied to irregular polygons? Why or why not?
5. How can you calculate the angle of rotation for any regular polygon?

Tip: To determine rotational symmetry, divide $360^\circ$ by the number of sides of the polygon!