Question

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

Explanation:

Step1: Recall rotational symmetry formula

For a regular polygon with \(n\) sides, the angle of rotation \(\theta\) that maps the polygon onto itself is given by \(\theta=\frac{360^{\circ}}{n}\).

Step2: Identify number of sides of hexagon

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

Step3: Calculate the angle of rotation

Substitute \(n = 6\) into the formula: \(\theta=\frac{360^{\circ}}{6}=60^{\circ}\). So a hexagon will map onto itself when rotated by \(60^{\circ}\), \(120^{\circ}\), \(180^{\circ}\) etc. The smallest such angle is \(60^{\circ}\).

Answer:

A. 60°