Question

5.
6.

1. a regular polygon has rotational symmetry with an order of 5 and a magnitude of 72°. what figure?

Explanation:

Step1: Recall rotational symmetry formula

For a regular polygon, the magnitude of rotational symmetry (angle of rotation) $\theta$ is given by $\theta=\frac{360^\circ}{n}$, where $n$ is the number of sides (and also the order of rotational symmetry).

Step2: Use given order to find sides

Given order of rotational symmetry is 5, so $n = 5$. A regular polygon with 5 sides is a pentagon. Also, check the angle: $\frac{360^\circ}{5}=72^\circ$, which matches the given magnitude.

Answer:

The figure is a regular pentagon.