Question

Determine the degree of rotation that would turn the figure onto itself.

Answer 1

To determine the degree of rotation that would turn a figure onto itself, you need to analyze the symmetry of the figure. The degree of rotation depends on the number of sides (or symmetry lines) the figure has.

Here’s a general guideline to find the degree of rotation:

1. **Identify the type of figure**: This could be a regular polygon (like a triangle, square, pentagon, etc.), a star shape, or any other symmetrical figure.

2. **Count the number of symmetrical positions**: For a regular polygon:
- A triangle (3 sides) has 3 symmetrical positions, so it can be rotated by \( \frac{360°}{3} = 120° \).
- A square (4 sides) has 4 symmetrical positions, so it can be rotated by \( \frac{360°}{4} = 90° \).
- A pentagon (5 sides) has 5 symmetrical positions, so it can be rotated by \( \frac{360°}{5} = 72° \).
- A hexagon (6 sides) has 6 symmetrical positions, so it can be rotated by \( \frac{360°}{6} = 60° \).

3. **Non-polygonal figures**: For figures like stars or other complex shapes, you would need to visually determine the symmetry.

Here’s a quick summary:
- Regular triangle: 120°
- Square: 90°
- Regular pentagon: 72°
- Regular hexagon: 60°

If you have a specific figure in mind, please describe it, and I can help you determine its degree of rotation!