Question

the measure of an interior angle of a regular polygon is given. find the number of sides in a polygon. show work. Number 8.

Answer 1

Given the following interior angle of a regular polygon:

$120\degree$

You need to remember that, by definition, a regular polygon is a polygon whose sides have all equal lengths.

Therefore, you can apply the following formula:

Where "n" is the number of sides of the polygon and β is the measure of one interior angle of the polygon.

Knowing that, in this case:

$\beta=120\degree$

Therefore, you can substitute this value into the formula and solve for "n":

$\begin{gathered} 120=\frac{(n-2)\cdot180}{n} \\ \\ 120n=180n-360 \end{gathered}$$\begin{gathered} 120n-180n=-360 \\ \\ -60n=-360 \\ \\ \\ n=\frac{-360}{-60} \end{gathered}$$n=6$

Hence, the answer is:

$n=6$