Question

10. Does rotating a dodecagon 540° result in a rotation onto itself? If so, how many times?How do you know?

Answer 1

A dodecagon has rotational symmetry of order 12 (has 12 sides)

`\begin{gathered} (360^o)/(12) \\ =30^o \end{gathered}`

This means that for every rotation of 30 degrees, the dodecagon results in a rotation onto itself. This includes all the degrees that are multiples of 30.

And, 540 degrees, is a multiple of 30, so a rotation of 540 degrees will result in a rotation onto itself.

To know how many times:

`\begin{gathered} (540)/(30) \\ 18\text{ times.} \end{gathered}`