Answer the following questions to summarize the rotations that carry a regular penagon onto itself. (4 points)

Question

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. \(288^\circ\).