Question
Find the sum of the interior angles of a 21-gon.
What is the sum of the exterior angles?
What is the sum of the exterior angles?
Answers
GPT-4o mini
To find the sum of the interior angles of a polygon, we use the formula:
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
where \( n \) is the number of sides of the polygon. For a 21-gon, we substitute \( n = 21 \):
\[
\text{Sum of interior angles} = (21 - 2) \times 180^\circ = 19 \times 180^\circ
\]
Calculating this gives:
\[
19 \times 180^\circ = 3420^\circ
\]
So, the sum of the interior angles of a 21-gon is \( 3420^\circ \).
Next, for the sum of the exterior angles of any polygon, there is a straightforward rule:
\[
\text{Sum of exterior angles} = 360^\circ
\]
This is true regardless of the number of sides of the polygon.
Therefore, for a 21-gon, the sum of the exterior angles is \( 360^\circ \).
In summary:
- The sum of the interior angles of a 21-gon is \( 3420^\circ \).
- The sum of the exterior angles of a 21-gon is \( 360^\circ \).
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
where \( n \) is the number of sides of the polygon. For a 21-gon, we substitute \( n = 21 \):
\[
\text{Sum of interior angles} = (21 - 2) \times 180^\circ = 19 \times 180^\circ
\]
Calculating this gives:
\[
19 \times 180^\circ = 3420^\circ
\]
So, the sum of the interior angles of a 21-gon is \( 3420^\circ \).
Next, for the sum of the exterior angles of any polygon, there is a straightforward rule:
\[
\text{Sum of exterior angles} = 360^\circ
\]
This is true regardless of the number of sides of the polygon.
Therefore, for a 21-gon, the sum of the exterior angles is \( 360^\circ \).
In summary:
- The sum of the interior angles of a 21-gon is \( 3420^\circ \).
- The sum of the exterior angles of a 21-gon is \( 360^\circ \).