Question

rotational symmetry does the figure have rotational symmetry? if so, state the degree measure of the angle of rotation.

Explanation:

Step1: Recall rotational - symmetry concept

A figure has rotational symmetry if it can be rotated about a point by an angle less than 360° and still look the same.

Step2: Analyze the star

A regular pentagram (five - pointed star) has rotational symmetry. The number of times it matches itself during a 360° rotation is equal to the number of its points. For a regular pentagram, \(n = 5\).

Step3: Calculate the angle of rotation

The formula for the angle of rotation \(\theta\) of a figure with \(n\) rotational symmetries is \(\theta=\frac{360^{\circ}}{n}\). Substituting \(n = 5\) into the formula, we get \(\theta=\frac{360^{\circ}}{5}=72^{\circ}\). But among the given options, we note the general concept of rotational symmetry for a star - like figure. A regular star with \(n\) points has rotational symmetry.

Answer:

YES, 72°