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Symmetry Quick Check 2 of 52 of 5 Items Question What is the smallest degree measure for a regular nonagon to rotate onto itself?(1 point) Responses 30° 30 degrees 60° 60 degrees 80° 80 degrees 40° 40 degrees Skip to navigation page 16 of 16
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GPT-4o mini
To find the smallest degree measure for a regular nonagon (a polygon with 9 sides) to rotate onto itself, you can use the formula for the angle of rotation that maps the polygon onto itself. This angle is given by:
\[
\text{Rotation Angle} = \frac{360°}{n}
\]
where \( n \) is the number of sides.
For a nonagon, \( n = 9 \):
\[
\text{Rotation Angle} = \frac{360°}{9} = 40°
\]
Therefore, the smallest degree measure for a regular nonagon to rotate onto itself is **40 degrees**.
\[
\text{Rotation Angle} = \frac{360°}{n}
\]
where \( n \) is the number of sides.
For a nonagon, \( n = 9 \):
\[
\text{Rotation Angle} = \frac{360°}{9} = 40°
\]
Therefore, the smallest degree measure for a regular nonagon to rotate onto itself is **40 degrees**.