To determine the sum of the interior angle measures of a polygon with 20 sides, we can use the formula for finding the sum of the interior angles of a polygon, which is given by:
[tex]\[ \text{Sum} = (n - 2) \times 180^\circ \][/tex]
where [tex]\( n \)[/tex] represents the number of sides of the polygon.
Let's break down the steps:
1. Identify the number of sides ([tex]\( n \)[/tex]) of the polygon. For this problem, [tex]\( n = 20 \)[/tex].
2. Substitute the value of [tex]\( n \)[/tex] into the formula:
[tex]\[ \text{Sum} = (20 - 2) \times 180^\circ \][/tex]
3. Simplify the expression within the parentheses:
[tex]\[ 20 - 2 = 18 \][/tex]
4. Multiply the result by [tex]\( 180^\circ \)[/tex]:
[tex]\[ 18 \times 180^\circ = 3240^\circ \][/tex]
Therefore, the sum of the interior angle measures of a polygon that has 20 sides is:
[tex]\[ \text{Sum} = 3240^\circ \][/tex]
