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?

(2 points)

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.

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

• 0 degrees (identity rotation)
• 72 degrees (one vertex to the next)
• 144 degrees (two vertices to the next)
• 216 degrees (three vertices to the next)
• 288 degrees (four vertices to the next)

b. Since a regular pentagon can make turns less than 360 degrees onto itself, it has rotational symmetry.