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.
Question 2
a. What are the degrees of the turns that will allow it to turn on itself?



b. Since a regular pentagon can make turns less than 360 degrees onto itself, it has what kind of symmetry?

Answer 1

To summarize the rotations that carry a regular pentagon onto itself:

Question 1: A regular pentagon can make 5 turns onto itself before coming around full circle. Each turn would be a multiple of 72 degrees (since \(360^\circ / 5 = 72^\circ\)).

Question 2:

a. The degrees of the turns that will allow it to turn on itself are:

• \(0^\circ\) (no turn),
• \(72^\circ\) (one turn),
• \(144^\circ\) (two turns),
• \(216^\circ\) (three turns),
• \(288^\circ\) (four turns).

b. Since a regular pentagon can make turns less than 360 degrees onto itself, it has rotational symmetry. This means that it can be rotated by certain angles and still look the same as its original position.