To find the sum of the measures of the interior angles of a decagon (a polygon with 10 sides), you can use the following formula:
Formula:
[tex]\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \][/tex]
where [tex]\( n \)[/tex] is the number of sides of the polygon.
For a decagon:
1. Substitute [tex]\( n = 10 \)[/tex] into the formula:
[tex]\[ \text{Sum of interior angles} = (10 - 2) \times 180^\circ \][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[ 10 - 2 = 8 \][/tex]
3. Multiply the result by 180 degrees:
[tex]\[ 8 \times 180^\circ = 1440^\circ \][/tex]
Thus, the sum of the measures of the interior angles of a decagon is [tex]\( \boldsymbol{1440^\circ} \)[/tex].
So, the correct answer is:
1440 degrees.
