Question

which of the following rotational symmetries apply to the regular octagon​

Answer 1

Answer:

Rotational symmetry of 135° about the origin: Yes

Rotational symmetry of 180° about the origin: Yes.

Step-by-step explanation:

Notice that the figure is a regular octagon, then, the figure has a rotational symmetry for multiple of 1/8 of a whole turn. To find the measure of the minimum angle of symmetry, divide 360 by 8:

$\frac{360}{8} = 45$

The regular octagon will have rotational symmetry about the origin for any angle which is multiple of 45°.

Divide 135° and 180° by 45° to check if they are multiples of 45°.

$\frac{135}{45} = 3 \\ \frac{180}{45} = 4$

Since both fractions are intengers, then both 135° and 180° are multiples of 45°.

Then, the regular octagon has rotational symmetry in both cases.

Therefore, the answer are;

Rotational symmetry of 135° about the origin: Yes

Rotational symmetry of 180° about the origin: Yes.