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

Sample answer for Edmentum and Plato users

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Answer 2

You can draw lines from the center of the hexagon to the peak. And you can find that this hexagon is divided to 6 parts. Every 60° can the hexagon map onto itself. So at 60,120,180,240,300 and 360 total 6 times.