Question

Answer the following questions to summarize the rotations that carry a regular penagon onto itself. (4 points)
A regular pentagon can make
turns onto itself before coming around full circle. Each turn would be a multiple of
degrees.

Answer 1

A regular pentagon has five sides, and it can be rotated onto itself a certain number of times before completing a full circle (360 degrees). Since there are 5 vertices, the rotations that carry the pentagon onto itself are determined by dividing 360 degrees by the number of vertices:

1. **Number of rotations**: A regular pentagon has 5 symmetrical rotations.
2. **Angle of each rotation**: Each rotation that carries the pentagon onto itself is a multiple of \( \frac{360}{5} = 72 \) degrees.

So in summary:
- A regular pentagon can make **5 turns** onto itself before coming around full circle.
- Each turn would be a multiple of **72 degrees**.

The specific rotations are:
1. \(0^\circ\) (no rotation),
2. \(72^\circ\),
3. \(144^\circ\),
4. \(216^\circ\),
5. \(288^\circ\).