Question
What is the smallest angle of rotational symmetry that maps a regular pentagon onto itself?
Enter your answer in the box.
Enter your answer in the box.
Answers
GPT-4o mini
The smallest angle of rotational symmetry that maps a regular pentagon onto itself can be calculated using the formula for the angle of symmetry in a regular polygon.
For a regular polygon with \( n \) sides, the smallest angle of rotational symmetry \( \theta \) is given by:
\[
\theta = \frac{360^\circ}{n}
\]
For a regular pentagon, \( n = 5 \). Therefore, we calculate:
\[
\theta = \frac{360^\circ}{5} = 72^\circ
\]
Thus, the smallest angle of rotational symmetry that maps a regular pentagon onto itself is
\[
\boxed{72}
\] degrees.
For a regular polygon with \( n \) sides, the smallest angle of rotational symmetry \( \theta \) is given by:
\[
\theta = \frac{360^\circ}{n}
\]
For a regular pentagon, \( n = 5 \). Therefore, we calculate:
\[
\theta = \frac{360^\circ}{5} = 72^\circ
\]
Thus, the smallest angle of rotational symmetry that maps a regular pentagon onto itself is
\[
\boxed{72}
\] degrees.