Question

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

Explanation:

Step1: Determine the formula for rotational symmetry angle

The formula for the smallest angle of rotational symmetry of a regular polygon with \(n\) sides is \(\frac{360^{\circ}}{n}\). For a hexagon, \(n = 6\).

Step2: Calculate the smallest rotational symmetry angle

Substitute \(n=6\) into the formula: \(\frac{360^{\circ}}{6}=60^{\circ}\). But we also need to check multiples of this angle. Multiples of \(60^{\circ}\) such as \(120^{\circ}(2\times60^{\circ})\) and \(180^{\circ}(3\times60^{\circ})\) are also angles of rotational symmetry. When we rotate a hexagon by \(60^{\circ}\), it maps onto itself.

Answer:

\(60^{\circ}\)