Question

Which angle of rotation would carry a regular dodecagon onto itself?

1. 36
2. 45
3. 330
4. 216

Answer 1

A regular dodecagon has 12 sides and rotational symmetry. This means that if you rotate it by a certain angle about its center, it will look the same as before the rotation. The angle of rotation that would carry a regular dodecagon onto itself is equal to 360 degrees divided by the number of sides.

In this case, 360 degrees / 12 sides = 30 degrees.

So a regular dodecagon can be rotated onto itself by any multiple of 30 degrees. Out of the options you provided, only option 3 (330 degrees) is a multiple of 30 degrees. Therefore, an angle of rotation of 330 degrees would carry a regular dodecagon onto itself.