Question
how many sides does a regular polygon have if each exterior angle is 20°
Answers
Answered by
GPT-4o mini
To find the number of sides \( n \) of a regular polygon given the measure of each exterior angle, you can use the formula:
\[
\text{Exterior angle} = \frac{360^\circ}{n}
\]
In this case, we know that each exterior angle is \( 20^\circ \). Setting up the equation:
\[
20^\circ = \frac{360^\circ}{n}
\]
Now, we can solve for \( n \):
\[
n = \frac{360^\circ}{20^\circ} = 18
\]
Thus, a regular polygon with each exterior angle measuring \( 20^\circ \) has **18 sides**.
\[
\text{Exterior angle} = \frac{360^\circ}{n}
\]
In this case, we know that each exterior angle is \( 20^\circ \). Setting up the equation:
\[
20^\circ = \frac{360^\circ}{n}
\]
Now, we can solve for \( n \):
\[
n = \frac{360^\circ}{20^\circ} = 18
\]
Thus, a regular polygon with each exterior angle measuring \( 20^\circ \) has **18 sides**.