Which angle of rotation is an angle of rotational symmetry for all figures?

Ask by Paul Mcfarlane. in the United States

Jan 23,2025

Question

Which angle of rotation is an angle of rotational symmetry for all figures? $$ 45^{\circ} $$ $$ 90^{\circ} $$ $$ 180^{\circ} $$ $$ 360^{\circ} $$

UpStudy AI · Accepted Answer

The **$$ 360^{\circ} $$** rotation is an angle of rotational symmetry for **all** figures.

Here's why:

- **$$ 360^{\circ} $$**: Rotating any figure by a full circle (360 degrees) brings it back to its original orientation. This is true for every possible shape, making it a universal angle of rotational symmetry.

- **Other angles (45°, 90°, 180°)**: These angles are only rotational symmetries for specific figures. For example:
  - **$$ 180^{\circ} $$**: Common in shapes like rectangles or certain triangles.
  - **$$ 90^{\circ} $$**: Typical in squares and some other regular polygons.
  - **$$ 45^{\circ} $$**: Found in shapes like octagons.

However, not all figures possess these rotational symmetries. Only the $$ 360^{\circ} $$ rotation guarantees symmetry for every possible figure.

**Answer:** $$ 360^{\circ} $$
All figures have rotational symmetry when rotated by $$ 360^{\circ} $$.

Which angle of rotation is an angle of rotational symmetry for all figures?

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