To determine the size of an interior angle of a regular polygon with 120 sides, follow these steps:
1. Understand the formula: The formula to calculate the interior angle of a regular polygon is:
[tex]\[
\text{interior angle} = \frac{(n - 2) \times 180^\circ}{n}
\][/tex]
where \( n \) is the number of sides of the polygon.
2. Substitute the number of sides into the formula: In this case, the polygon has 120 sides. Therefore, substitute \( n = 120 \) into the formula.
[tex]\[
\text{interior angle} = \frac{(120 - 2) \times 180^\circ}{120}
\][/tex]
3. Simplify the subtraction:
[tex]\[
120 - 2 = 118
\][/tex]
So the formula now looks like:
[tex]\[
\text{interior angle} = \frac{118 \times 180^\circ}{120}
\][/tex]
4. Calculate the multiplication:
[tex]\[
118 \times 180 = 21240^\circ
\][/tex]
5. Divide by the number of sides:
[tex]\[
\frac{21240^\circ}{120} = 177^\circ
\][/tex]
Thus, the size of an interior angle of a regular polygon with 120 sides is [tex]\( 177^\circ \)[/tex].
