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 $135^{\circ}$ about the origin

Rotational symmetry of $180^{\circ}$ about the origin
Applies to the figure?
Yes/No
Yes/No

Question

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 $135^{\circ}$ about the origin

Rotational symmetry of $180^{\circ}$ about the origin
Applies to the figure?
Yes/No
Yes/No

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ A regular octagon has rotational symmetries at multiples of $45^\circ$. ‖ ‖ step 2 ⋮ To determine if the octagon has rotational symmetry of $135^\circ$, we check if $135^\circ$ is a multiple of $45^\circ$. ‖ ‖ step 3 ⋮ $135^\circ = 3 imes 45^\circ$, so the octagon has rotational symmetry of $135^\circ$. ‖ ‖ step 4 ⋮ To determine if the octagon has rotational symmetry of $180^\circ$, we check if $180^\circ$ is a multiple of $45^\circ$. ‖ ‖ step 5 ⋮ $180^\circ = 4 imes 45^\circ$, so the octagon has rotational symmetry of $180^\circ$. ‖ ***Yes, Yes*** ∻Key Concept∻ ⚹Rotational Symmetry⚹ ∻Explanation∻ ⚹A regular octagon has rotational symmetries at multiples of $45^\circ$. Therefore, it has rotational symmetries at $135^\circ$ and $180^\circ$.⚹◊What is the formula to calculate the rotational symmetry of a regular octagon?⍭ Generate me a similar question◊

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