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:
- Recognize that a regularagon has identical sides and.
- The symmetry rotations are spaced around the circle, dividing $360°$ into 6 parts.
- 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°$.