Question
Find the sum of the measures of the interior angles of the regular nonagon.
Answers
GPT-4o mini
To find the sum of the measures of the interior angles of a polygon, we can 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 nonagon, which has 9 sides, we substitute \( n = 9 \):
\[
\text{Sum of interior angles} = (9 - 2) \times 180^\circ
\]
Calculating this gives:
\[
\text{Sum of interior angles} = 7 \times 180^\circ = 1260^\circ
\]
Thus, the sum of the measures of the interior angles of a regular nonagon is
\[
\boxed{1260^\circ}
\]
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
where \( n \) is the number of sides of the polygon.
For a nonagon, which has 9 sides, we substitute \( n = 9 \):
\[
\text{Sum of interior angles} = (9 - 2) \times 180^\circ
\]
Calculating this gives:
\[
\text{Sum of interior angles} = 7 \times 180^\circ = 1260^\circ
\]
Thus, the sum of the measures of the interior angles of a regular nonagon is
\[
\boxed{1260^\circ}
\]