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. 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)

Explanation:

Step1: Determine number of turns

A regular pentagon has 5 congruent sides and 5 congruent angles. The number of times it can map onto itself before a full - 360 - degree rotation is equal to the number of its sides. So it can make 4 turns onto itself before coming around full circle (excluding the 360 - degree rotation which is a full circle).

Step2: Calculate angle of each turn

The total angle of a full - circle rotation is 360 degrees. For a regular pentagon, to find the angle of rotation that maps it onto itself, we divide 360 by the number of sides (n = 5). So the angle of each turn is $\frac{360}{5}=72$ degrees. The angles of rotation that map it onto itself are multiples of 72 degrees: 72°, 144°, 216°, 288°.

Step3: Identify type of symmetry

Since a regular pentagon can be rotated by an angle less than 360 degrees and map onto itself, it has rotational symmetry.

Answer:

A regular pentagon can make 4 turns onto itself before coming around full circle. Each turn would be a multiple of 72 degrees.
a. The degrees of the turns that will allow it to turn on itself are 72°, 144°, 216°, 288°.
b. It has rotational symmetry.