Question

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

Answer 1

The polygon has 5 sides;

`n=5`

Step-by-step explanation:

The measure of an interior angles of a regular polygon can be given by the formula;

`x=((n-2)180)/(n)`

Where;

n = number of sides of the polygon

x = measure of each interior angle of the polygon

Given;

4.

`x=108`

substituting into the formula and solving for n, we have;

`\begin{gathered} x=((n-2)180)/(n) \\ 108=((n-2)180)/(n) \\ \text{cross multiply and expand;} \\ 108n=180n-360 \\ 180n-108n=360 \\ 72n=360 \\ n=(360)/(72) \\ n=5 \end{gathered}`

Therefore, the polygon has 5 sides;

`n=5`