Question

provide two different degrees of rotation less than 150° but greater than 0° that will turn a regular pentagon onto itself. (1 point)
a regular pentagon will turn onto itself after a and rotation.

Explanation:

Step1: Calculate the angle of rotational symmetry

For a regular \(n -\)sided polygon, the angle of rotational symmetry \(\theta=\frac{360^{\circ}}{n}\). For a pentagon, \(n = 5\), so \(\theta=\frac{360^{\circ}}{5}=72^{\circ}\).

Step2: Find multiples of the angle of rotational symmetry

The rotations that map a regular pentagon onto itself are multiples of \(72^{\circ}\). The first - multiple is \(72^{\circ}\), and the second - multiple is \(2\times72^{\circ}=144^{\circ}\), and both \(72^{\circ}\) and \(144^{\circ}\) are between \(0^{\circ}\) and \(150^{\circ}\).

Answer:

72, 144