Question
What is the smallest degree measure for a regular nonagon to rotate onto itself?
a. 40 degree
b. 80 degree
c. 60 degree
d. 30 degree
a. 40 degree
b. 80 degree
c. 60 degree
d. 30 degree
Answers
Answered by
GPT-4o mini
To determine the smallest degree measure for a regular nonagon to rotate onto itself, we first need to understand the properties of a regular nonagon.
A regular nonagon has 9 sides, and it can rotate in incremental angles based on the total degrees in a circle (360 degrees) divided by the number of sides (9). Thus, the angle of rotation for the nonagon is calculated as follows:
\[
\text{Angle of rotation} = \frac{360^\circ}{9} = 40^\circ
\]
This means that rotating the nonagon by 40 degrees will map it onto itself. Therefore, for the nonagon, the smallest degree measure for it to rotate onto itself is:
\[
\boxed{40}
\]
Thus, the answer is (a) 40 degrees.
A regular nonagon has 9 sides, and it can rotate in incremental angles based on the total degrees in a circle (360 degrees) divided by the number of sides (9). Thus, the angle of rotation for the nonagon is calculated as follows:
\[
\text{Angle of rotation} = \frac{360^\circ}{9} = 40^\circ
\]
This means that rotating the nonagon by 40 degrees will map it onto itself. Therefore, for the nonagon, the smallest degree measure for it to rotate onto itself is:
\[
\boxed{40}
\]
Thus, the answer is (a) 40 degrees.