To find the sum of the measures of the interior angles of a polygon, you can use the following formula for an [tex]\( n \)[/tex]-sided polygon (or [tex]\( n \)[/tex]-gon):
[tex]\[
\text{Sum of the interior angles} = (n - 2) \times 180^{\circ}
\][/tex]
where [tex]\( n \)[/tex] is the number of sides of the polygon.
Let's use this formula to find the sum of the interior angles for a 12-sided polygon (12-gon):
1. Determine the number of sides, [tex]\( n \)[/tex], which is 12 in this case.
2. Substitute [tex]\( n = 12 \)[/tex] into the formula:
[tex]\[
\text{Sum of the interior angles} = (12 - 2) \times 180^{\circ}
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
(12 - 2) = 10
\][/tex]
4. Multiply by 180 degrees:
[tex]\[
10 \times 180^{\circ} = 1800^{\circ}
\][/tex]
Therefore, the sum of the measures of the interior angles of a 12-gon is [tex]\( 1800^{\circ} \)[/tex].
The correct answer is [tex]\( 1800^{\circ} \)[/tex].
