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What is the sum of the measures of the interior angles of a 12-gon?
A. [tex]$1620^{\circ}$[/tex] B. [tex]$1800^{\circ}$[/tex] C. [tex]$1980^{\circ}$[/tex] D. [tex]$2160^{\circ}$[/tex]
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]
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