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The question asks for the rotations that map an equilateral triangle onto itself, with angles less than or equal to \(360^\circ\).

To solve this:

1. An equilateral triangle has 3 sides.
2. The smallest angle of rotation that will map the triangle onto itself is found by dividing \(360^\circ\) by the number of sides, which is:
   \[
   \frac{360^\circ}{3} = 120^\circ.
   \]
3. Now, the valid rotation angles are multiples of \(120^\circ\) that are less than or equal to \(360^\circ\):
   - \(120^\circ\)
   - \(240^\circ\)
   - \(360^\circ\)

Thus, the rotations are \(120^\circ\), \(240^\circ\), and \(360^\circ\).

Would you like further details or explanations?

Here are 5 related questions you can explore:
1. What are the rotation symmetries of a square?
2. How do you calculate the rotational symmetry of any regular polygon?
3. What is the difference between rotational and reflectional symmetry in polygons?
4. How do rotational angles change for polygons with more sides?
5. What is the center of rotation for regular polygons?

**Tip:** Rotational symmetry of a regular polygon is determined by the number of sides. The number of unique rotations is always equal to the number of sides.

Describe any rotations less than or equal to 360° that map the equilateral triangle onto itself.

Explore the rotational symmetries of an equilateral triangle. Learn how to calculate the angles that map the triangle onto itself using the formula 360° divided by the number of sides. Suitable for middle school students in grades 6-8.

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