at which angle will the hexagon rotate so that it maps onto itself?\n60°\n90°\n120°\n180°

Explanation:

Step1: Recall rotational - symmetry formula

For a regular (n) - sided polygon, the angle of rotation (\theta) that maps the polygon onto itself is given by (\theta=\frac{360^{\circ}}{k}), where (k) is a positive integer and (k\leq n). For a regular hexagon, (n = 6).

Step2: Calculate the smallest non - zero angle of rotation

The smallest non - zero value of (k) for which the hexagon rotates onto itself is (k = 1), and (\theta=\frac{360^{\circ}}{6}=60^{\circ}). Also, multiples of (60^{\circ}) will map the hexagon onto itself. Among the given options (60^{\circ},90^{\circ},120^{\circ},180^{\circ}), all of (60^{\circ},120^{\circ},180^{\circ}) are angles of rotation that map the hexagon onto itself, but the question asks for an angle. The most basic non - zero angle of rotation for a hexagon is (60^{\circ}).

Answer:

A. (60^{\circ})