Question

A regular hexagon rotates counterclockwise about its center. It turns through angles greater than 0° and less than or equal to 360°. At how many different angles will the hexagon map onto itself??

Answer 1

A hexagon has 6 sides, and 1/6 of 360 degrees is 60 degrees, so every 60 degrees the hexagon will map onto itself.

Answer 2

6 different angles.

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
`60^(\circ), 120^(\circ), 180^(\circ), 240^(\circ), 300^(\circ), 360^(\circ)`.