Question

Which statements are true regarding the regular dodecagon? Check all that apply.

The smallest angle of rotational symmetry for the dodecagon is 30°.
The dodecagon has a rotational symmetry of 180°.
The order of rotational symmetry for the dodecagon is 10.
The dodecagon has a rotational symmetry of 135°.
The angles of rotational symmetry for the dodecagon are multiples of 30°.

Answer 1

A dodecagon has 12 sides.  That means that the smallest angle of rotational symmetry is 360/12 or 30°.  All of its angles of rotational symmetry will be multiples of 30, including 180°.  135°, since it is not a multiple of 30°, is not a rotational angle for this figure.  The order of °rotational symmetry is 12, as there are 12 sides you can turn this figure to (since it is regular).

Answer 2

The statements that can be inferred to be true regarding the regular dodecagon include:

• The smallest angle of rotational symmetry for the dodecagon is 30°.
• The dodecagon has a rotational symmetry of 180°.
• The angles of rotational symmetry for the dodecagon are multiples of 30°.

A dodecagon simply means a twelve-sided star polygon that encloses space. It can be regular when all the interior angles and sides are equal.

It should be noted that the smallest angle of rotational symmetry for the dodecagon is 30° and it has a rotational symmetry of 180.

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