Questions: The center of the regular hexagon below is at the origin. Which of the following rotational symmetries apply to the regular hexagon? Rotation Applies to the figure? Rotational symmetry of 60 degrees about the origin Yes / No ∨ Rotational symmetry of 120 degrees about the origin Yes / No ∨

The center of the regular hexagon below is at the origin.

Which of the following rotational symmetries apply to the regular hexagon?

Rotation Applies to the figure?

Rotational symmetry of 60 degrees about the origin Yes / No ∨

Rotational symmetry of 120 degrees about the origin Yes / No ∨

Transcript text: The center of the regular hexagon below is at the origin. Which of the following rotational symmetries apply to the regular hexagon? \begin{tabular}{lc} Rotation & Applies to the figure? \\ \hline Rotational symmetry of $60^{\circ}$ about the origin & $Y e s / \mathrm{No} \vee$ \\ Rotational symmetry of $120^{\circ}$ about the origin & $\mathrm{Yes} / \mathrm{No} \vee$ \end{tabular}

Solution

Solution Steps

Step 1: Determine the angles of rotational symmetry for a regular hexagon

A regular hexagon has 6 sides. A full rotation is 360°. The angles of rotational symmetry can be found by dividing 360° by the number of sides. So, 360°/6 = 60°. Multiples of 60° will also be angles of rotational symmetry.

Step 2: Evaluate the given angles

The problem asks if the hexagon has rotational symmetry of 60° and 120° about the origin. Since 60° is an angle of rotational symmetry for a hexagon, and 120° is a multiple of 60° (2 * 60° = 120°), both of these angles represent rotational symmetry.