Certainly! Let's determine the sum of the interior angles of a 12-sided polygon, also known as a 12-gon.
To find the sum of the interior angles of any [tex]\( n \)[/tex]-gon, you can use the formula:
[tex]\[ \text{Sum of the interior angles} = (n - 2) \times 180^\circ \][/tex]
Here, [tex]\( n \)[/tex] represents the number of sides of the polygon.
For a 12-gon, [tex]\( n = 12 \)[/tex].
Plug [tex]\( n = 12 \)[/tex] into the formula:
[tex]\[ \text{Sum of the interior angles} = (12 - 2) \times 180^\circ \][/tex]
First, simplify inside the parentheses:
[tex]\[ 12 - 2 = 10 \][/tex]
Next, multiply by [tex]\( 180^\circ \)[/tex]:
[tex]\[ 10 \times 180^\circ = 1800^\circ \][/tex]
So, the sum of the measures of the interior angles of a 12-gon is:
[tex]\[ \boxed{1800^\circ} \][/tex]
Therefore, the answer is [tex]\( 1800^\circ \)[/tex].
