what is the smallest angle of rotational symmetry that maps a regular nonagon onto itself?

A regular nonagon has 9 sides. The smallest angle of rotational symmetry that maps a regular polygon onto itself is given by the formula:

\[
\text{Smallest angle} = \frac{360^\circ}{n}
\]

where \( n \) is the number of sides of the polygon.

For a nonagon, \( n = 9 \). Therefore, the smallest angle of rotational symmetry is:

\[
\frac{360^\circ}{9} = 40^\circ
\]

Thus, the smallest angle of rotational symmetry that maps a regular nonagon onto itself is **40 degrees**.

Would you like further details or have any questions?

Here are 5 related questions:
1. What are the other angles of rotational symmetry for a regular nonagon?
2. How many lines of symmetry does a regular nonagon have?
3. What is the sum of the interior angles of a regular nonagon?
4. How do you find the interior and exterior angles of a regular polygon?
5. What is the area of a regular nonagon with a given side length?

**Tip:** The number of lines of symmetry in a regular polygon is equal to the number of sides of the polygon.

What is the smallest angle of rotational symmetry that maps a regular nonagon onto itself?

Learn how to find the smallest angle of rotational symmetry for a regular nonagon using the formula 360°/n. This problem involves concepts like polygon properties and symmetry, making it ideal for students in Grades 6-8. Understand the detailed steps and explore related symmetry properties for other polygons.

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