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 Order

The order of rotational symmetry of a regular polygon is equal to the number of its sides (\(n\)). Here, the order is 5, so \(n = 5\).

Step2: Recall Rotational Magnitude Formula

The magnitude of rotational symmetry (angle of rotation) for a regular polygon is given by \(\frac{360^\circ}{n}\). Substituting \(n = 5\), we get \(\frac{360^\circ}{5}=72^\circ\), which matches the given magnitude.

Step3: Identify the Polygon

A regular polygon with 5 sides is a regular pentagon.

Answer:

The figure is a regular pentagon.