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

Hence, the answer is:

`n=6`