Question

b. 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 rotational symmetry. This means that it can be rotated about its center by certain angles (less than 360 degrees) and still appear unchanged. Specifically, a regular pentagon can be rotated by angles of \(72\) degrees (which is \(360/5\)), \(144\) degrees, \(216\) degrees, and \(288\) degrees, in addition to a full \(360\) degrees, and it will still look the same. In addition to rotational symmetry, a regular pentagon also has reflectional symmetry, as it can be reflected across lines that pass through its vertices and midpoints of its sides.