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 $135^{\circ}$ about the origin
Rotational symmetry of $180^{\circ}$ 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 $135^\circ$, we check if $135^\circ$ is a multiple of $45^\circ$

step 3

$135^\circ = 3 \times 45^\circ$, 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

$180^\circ = 4 \times 45^\circ$, 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 $180^\circ$.

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