Answer:
6 different angles.
Step-by-step explanation:
We have been given that a regular hexagon rotates counterclockwise about its center. It turns through angles greater than 0° and less than or equal to 360°
We know that each interior angle of a regular hexagon equals 60 degrees, so with each rotation of 60 degrees, the hexagon will map onto itself.
The multiples of 60 between 0 and 360 are: 60, 120, 180, 240, 300, 360.
Therefore, the hexagon will map onto itself at 6 different angles that are [tex]60^{\circ}, 120^{\circ}, 180^{\circ}, 240^{\circ}, 300^{\circ}, 360^{\circ}[/tex].
