regular hexagon makes L

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turns onto itself before
coming around full circle. Each rotation is a multiple of
degrees.
B) What are the degrees of turns that allow the regular hexagon to turn onto itself? Check ALL that apply (1 point)
• 30
60
90
120
150
180
• 210
240
• 270
• 300
• 330

1 answer

A regular hexagon can be turned onto itself when the angle of rotation is a multiple of the angles between its vertices. The angle between adjacent vertices of a regular hexagon is:

\[ \frac{360^\circ}{6} = 60^\circ. \]

Thus, the hexagon will turn onto itself for any multiple of this angle:

  • 0° (no turn)
  • 60° (1 vertex turn)
  • 120° (2 vertex turns)
  • 180° (3 vertex turns)
  • 240° (4 vertex turns)
  • 300° (5 vertex turns)

These angles can be represented as \( n \times 60^\circ \), where \( n \) is an integer from 0 to 5.

From your list, the degrees of turns that allow the regular hexagon to turn onto itself are:

  • 60
  • 120
  • 180
  • 240
  • 300

The other angles (30, 90, 150, 210, 270, and 330) do not align with the symmetry of the hexagon and thus do not rotate it onto itself.

So, the correct answers are:

  • 60
  • 120
  • 180
  • 240
  • 300