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]



Answer :

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]