To find the sum of the measures of the interior angles of a decagon, we first need to understand some basic properties of polygons.
A decagon is a polygon with 10 sides. The formula to find the sum of the interior angles of a polygon with [tex]\( n \)[/tex] sides is given by:
[tex]\[
(n - 2) \times 180^\circ
\][/tex]
where [tex]\( n \)[/tex] is the number of sides of the polygon.
For a decagon ([tex]\( n = 10 \)[/tex]):
1. Substitute [tex]\( n = 10 \)[/tex] into the formula:
[tex]\[
(10 - 2) \times 180^\circ
\][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[
8 \times 180^\circ
\][/tex]
3. Multiply the numbers:
[tex]\[
1440^\circ
\][/tex]
Therefore, the sum of the measures of the interior angles of a decagon is [tex]\( 1440^\circ \)[/tex].
The correct answer is:
C. 1440°
