Question

determine whether each figure has a line of symmetry. if so, draw the lines of symmetry and state how many lines of symmetry it has.
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1. a regular polygon has rotational symmetry with an order of 5 and a magnitude of 72°. what is the figure?

Explanation:

Step1: Recall rotational symmetry formula

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

Step2: Substitute given values

We know $\theta = 72^\circ$ and order $n = 5$. Using the formula $\theta=\frac{360^\circ}{n}$, substitute $n = 5$: $\frac{360^\circ}{5}=72^\circ$, which matches the given magnitude. A regular polygon with $n = 5$ sides is a regular pentagon.

Answer:

Regular Pentagon