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Question
Math
Posted 2 months ago

The center of the regular octagon below is at the origin.

Which of the following rotational symmetries apply to the regular octagon?

Rotation

Rotational symmetry of 135135^{\circ} about the origin

Rotational symmetry of 180180^{\circ} about the origin
Applies to the figure?
Yes/No
Yes/No
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 2
To determine if the octagon has rotational symmetry of 135135^\circ, we check if 135135^\circ is a multiple of 4545^\circ
step 3
135=3×45135^\circ = 3 \times 45^\circ, so the octagon has rotational symmetry of 135135^\circ
step 4
To determine if the octagon has rotational symmetry of 180180^\circ, we check if 180180^\circ is a multiple of 4545^\circ
step 5
180=4×45180^\circ = 4 \times 45^\circ, so the octagon has rotational symmetry of 180180^\circ
Yes, Yes
Key Concept
Rotational Symmetry
Explanation
A regular octagon has rotational symmetries at multiples of 4545^\circ. Therefore, it has rotational symmetries at 135135^\circ and 180180^\circ.

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