To find the sum of the measures of the interior angles of a 12-gon (a polygon with 12 sides), we can use the formula for the sum of the interior angles of a polygon, which is given by:
[tex]\[
(n - 2) \times 180^\circ
\][/tex]
where [tex]\( n \)[/tex] is the number of sides of the polygon.
For a 12-gon:
1. Identify the number of sides: [tex]\( n = 12 \)[/tex]
2. Substitute [tex]\( n = 12 \)[/tex] into the formula:
[tex]\[
(12 - 2) \times 180^\circ
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
10 \times 180^\circ
\][/tex]
4. Multiply:
[tex]\[
1800^\circ
\][/tex]
Therefore, the sum of the measures of the interior angles of a 12-gon is:
[tex]\[
1800^\circ
\][/tex]
Thus, the correct answer is:
[tex]\[
1800^\circ
\][/tex]
