Question
What is the sum of the exterior angles of a regular 24-gon?
What is the measure of EACH exterior angle?
What is the measure of EACH exterior angle?
Answers
Answered by
GPT-4o mini
The sum of the exterior angles of any polygon is always \(360\) degrees, regardless of the number of sides. Therefore, for a regular 24-gon, the sum of the exterior angles is:
\[
\text{Sum of exterior angles} = 360^\circ
\]
To find the measure of each exterior angle in a regular 24-gon, we can use the following formula:
\[
\text{Measure of each exterior angle} = \frac{\text{Sum of exterior angles}}{\text{Number of sides}}
\]
Since the number of sides (or vertices) for the 24-gon is \(24\), we can calculate:
\[
\text{Measure of each exterior angle} = \frac{360^\circ}{24} = 15^\circ
\]
Thus, the measure of each exterior angle in a regular 24-gon is \(15\) degrees.
In summary:
- The sum of the exterior angles is \(360^\circ\).
- The measure of each exterior angle is \(15^\circ\).
\[
\text{Sum of exterior angles} = 360^\circ
\]
To find the measure of each exterior angle in a regular 24-gon, we can use the following formula:
\[
\text{Measure of each exterior angle} = \frac{\text{Sum of exterior angles}}{\text{Number of sides}}
\]
Since the number of sides (or vertices) for the 24-gon is \(24\), we can calculate:
\[
\text{Measure of each exterior angle} = \frac{360^\circ}{24} = 15^\circ
\]
Thus, the measure of each exterior angle in a regular 24-gon is \(15\) degrees.
In summary:
- The sum of the exterior angles is \(360^\circ\).
- The measure of each exterior angle is \(15^\circ\).