A regular hexagon has rotational symmetry. Name the largest degree of rotation, excluding 360degrees, that would turn a regular hexagon onto itself.

Question

A rotation of ___degrees would turn a regular hexagon onto itself

Answer 1

A regular hexagon has rotational symmetry of order 6. This means it can be rotated by certain angles and still appear the same. The angles of rotation that will not change the appearance of the hexagon are obtained by dividing 360 degrees by the number of sides:

\[ \text{Rotation angles} = \frac{360^\circ}{6} = 60^\circ \]

The angles that will turn the hexagon onto itself are:

• 0 degrees (no rotation)
• 60 degrees
• 120 degrees
• 180 degrees
• 240 degrees
• 300 degrees

Excluding 360 degrees (which is effectively no rotation), the largest degree of rotation that would turn a regular hexagon onto itself is:

\[ \boxed{300} \text{ degrees} \]