To find the sum of the interior angles of a pentagon, we can use a well-known formula for the sum of the interior angles of any polygon.
The formula for finding 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] represents the number of sides.
Step-by-step solution:
1. Determine the number of sides in a pentagon:
- A pentagon has 5 sides.
2. Substitute the number of sides into the formula:
[tex]\[
(5 - 2) \times 180^\circ
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
3 \times 180^\circ
\][/tex]
4. Multiply the numbers:
[tex]\[
540^\circ
\][/tex]
Thus, the sum of the interior angles of a pentagon is [tex]\( 540^\circ \)[/tex].
The correct answer from the given options is:
[tex]\[
540^\circ
\][/tex]
