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

Question

A rotation of ___ degree would turn a regular hexagon on itself

Answer 1

A regular hexagon has rotational symmetry of order 6, meaning it can be rotated in multiples of \(360^\circ / 6 = 60^\circ\).

The degrees of rotation that will map a regular hexagon onto itself are:

• \(0^\circ\)
• \(60^\circ\)
• \(120^\circ\)
• \(180^\circ\)
• \(240^\circ\)
• \(300^\circ\)

Excluding \(360^\circ\), the largest degree of rotation that would turn a regular hexagon onto itself is \(300^\circ\).

Thus, a rotation of 300 degrees would turn a regular hexagon on itself.