What is the minimum number of degrees that a regular hexagon can be rotated before it carries onto itself?A.180B.90C.60D.45SUBMITarrow_backPREVIOUS

1. Break Down the Problem

To determine the minimum number of degrees a regular hexagon can be rotated before it appears the same as its original position, we need to analyze the symmetry of the hexagon.

2. Relevant Concepts

A regular hexagon has 6 equal sides and 6 equal angles. The rotational symmetry can be calculated by the formula:

$\text{Rotation Angle} = \frac{360^\circ}{n}$

where $n$ is the number of sides (or vertices) of the polygon.

3. Analysis and Detail

For a regular hexagon, $n = 6$. Therefore, the minimum rotation angle for it to carry onto itself can be calculated as follows:

$\text{Rotation Angle} = \frac{360^\circ}{6} = 60^\circ$

This means that rotating the hexagon by 60 degrees will align it with its original position.

4. Verify and Summarize

Since 60 degrees is the calculated angle and it is indeed one of the options given, we can conclude confidently.

Final Answer

The minimum number of degrees that a regular hexagon can be rotated before it carries onto itself is $\boxed{60}$ (Option C).