Question

at which angle will the hexagon rotate so that it maps onto itself? 60° 90° 120° 180°

Explanation:

Step1: Recall the formula for rotational symmetry

The formula for the angle of rotational symmetry of a regular polygon is \(\frac{360^{\circ}}{n}\), where \(n\) is the number of sides.

Step2: Identify \(n\) for a hexagon

A hexagon has \(n = 6\) sides.

Step3: Calculate the angle

Substitute \(n=6\) into the formula: \(\frac{360^{\circ}}{6}=60^{\circ}\). Also, multiples of \(60^{\circ}\) (such as \(120^{\circ},180^{\circ}\)) will also map the hexagon onto itself. But \(60^{\circ}\) is the smallest such angle among the given options.

Answer:

\(60^{\circ}\)