A regular pentagon can make ____ turns onto itself before coming around full circle. Each turn would be a multiple of ___ degrees.

Question

what are the degrees of the turns that will allow it to turn on itself?
since a regular pentagon can make turns less than 360 degrees onto itself? It has what kind of symmetry?

Answer 1

A regular pentagon has 5 sides, and it can make 4 distinct turns onto itself before completing a full circle (360 degrees). These turns are determined by the angles between adjacent vertices, which can be described as rotations.

1. Turns: The number of turns a regular pentagon can make onto itself before coming around full circle is 5 turns (including the one full turn which is 360 degrees).

2. Multiple of Degrees: Each turn that results in the pentagon appearing identical to its original position corresponds to \( \frac{360}{5} = 72 \) degrees. Therefore, it can make turns of 72 degrees, 144 degrees, 216 degrees, and 288 degrees, in addition to the full turn (360 degrees).

3. Symmetry: Since a regular pentagon can make turns less than 360 degrees onto itself, it exhibits rotational symmetry. Specifically, it has rotational symmetry of order 5, meaning it looks the same at every \( 72 \) degrees of rotation around its center.

In summary:

• A regular pentagon can make 4 turns onto itself before coming around full circle.
• Each of these turns is a multiple of 72 degrees.
• It has rotational symmetry of order 5.