At which angle will the hexagon rotate so that it maps onto itself?

At which angle will the hexagon rotate so that it maps onto itself?

Answer

hexagon will onto at an angle of 60°.

Explanation

A hexagon has rotational symmetry of order6, meaning it maps onto itself after rotations of multiples $60°$ (since $360°/6 60°$). These rotations include $60° $120°$, $° $°$, $300°$, and $0°$ (a full rotation:

  1. Recognize that a regularagon has identical sides and.
  2. The symmetry rotations are spaced around the circle, dividing $360°$ into 6 parts.
  3. Therefore, the smallest non-zero angle for which the hexagon maps onto itself is $60°$.

Hence, the hexagon will map itself when rotated by 60°$.