Question
How many sides does a polygon have with each exterior angle being 22.5
Answers
GPT-4o mini
To find the number of sides \( n \) of a polygon based on the measure of its exterior angles, you can use the formula for the exterior angle of a regular polygon, which states that the sum of all exterior angles of a polygon is always \( 360^\circ \). The measure of each exterior angle \( E \) of a regular polygon is given by:
\[
E = \frac{360^\circ}{n}
\]
where \( n \) is the number of sides of the polygon. If each exterior angle is \( 22.5^\circ \), we can set up the equation:
\[
22.5 = \frac{360}{n}
\]
To solve for \( n \), we can rearrange the equation:
\[
n = \frac{360}{22.5}
\]
Now, we will calculate \( n \):
\[
n = \frac{360}{22.5} = 16
\]
Thus, a polygon with each exterior angle measuring \( 22.5^\circ \) has \( 16 \) sides.
The answer is:
\[
\boxed{16}
\]
\[
E = \frac{360^\circ}{n}
\]
where \( n \) is the number of sides of the polygon. If each exterior angle is \( 22.5^\circ \), we can set up the equation:
\[
22.5 = \frac{360}{n}
\]
To solve for \( n \), we can rearrange the equation:
\[
n = \frac{360}{22.5}
\]
Now, we will calculate \( n \):
\[
n = \frac{360}{22.5} = 16
\]
Thus, a polygon with each exterior angle measuring \( 22.5^\circ \) has \( 16 \) sides.
The answer is:
\[
\boxed{16}
\]