Question

A regular hexagon makes
turns onto itself before coming around full circle. Each rotation is a multiple of
degrees.
Question 2
What are the degrees of turns that allow the regular hexagon to turn onto itself? Check ALL that apply(1 point)
Responses

30
30

60
60

90
90

120
120

150
150

180
180

210
210

240
240

270
270

300
300

330
330

360

Answer 1

A regular hexagon has rotational symmetry and can rotate onto itself at specific angles corresponding to its internal symmetry. The full rotation of a hexagon is 360 degrees, and it can be turned onto itself in multiples of 360 degrees divided by the number of sides.

For a regular hexagon (which has 6 sides), the possible angles of rotation that allow it to coincide with its original position are given by:

\[
\text{Angles} = \frac{360^\circ}{6} \times n \quad \text{where } n = 0, 1, 2, ..., 5
\]

This results in the following angles:

- \( n = 0 \): \( 0^\circ \)
- \( n = 1 \): \( 60^\circ \)
- \( n = 2 \): \( 120^\circ \)
- \( n = 3 \): \( 180^\circ \)
- \( n = 4 \): \( 240^\circ \)
- \( n = 5 \): \( 300^\circ \)

Thus, the angles of rotation that allow the regular hexagon to turn onto itself are:

- **60**
- **120**
- **180**
- **240**
- **300**

Therefore, the correct responses are:

- **60**
- **120**
- **180**
- **240**
- **300**