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?

Question

aum · Answer

A regular hexagon has 6 equal sides and each side makes an angle of 360/6 = 60 degrees at the center.  So if the hexagon is turned 60 degrees, the first side will coincide with the second side, the second side with the third side, etc.  So each time you turn the hexagon by 60 degrees the hexagon will map onto itself.  So how many 60 degrees are there in 360 degrees?