Question

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
360
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Answer 1

To determine the degrees of turns that allow a regular hexagon to turn onto itself, we need to look at the angles based on its symmetries. A regular hexagon has 6 rotational symmetries, which means it can be rotated through angles that are multiples of \( \frac{360°}{6} = 60° \).

The valid angles are therefore:

- \( 0° \) (no rotation)
- \( 60° \)
- \( 120° \)
- \( 180° \)
- \( 240° \)
- \( 300° \)
- \( 360° \) (full rotation)

From the given options, the angles that satisfy these conditions and allow the hexagon to map onto itself are:

- \( 60° \)
- \( 120° \)
- \( 180° \)
- \( 240° \)
- \( 300° \)
- \( 360° \)

So the correct selections are:

- 60
- 120
- 180
- 240
- 300
- 360

Options such as \( 30, 90, 150, 210, 270, \) and \( 330 \) do not map the hexagon onto itself, so they are not correct.