Answer:
The polygon has 5 sides;
[tex]n=5[/tex]
Explanation:
The measure of an interior angles of a regular polygon can be given by the formula;
[tex]x=\frac{(n-2)180}{n}[/tex]
Where;
n = number of sides of the polygon
x = measure of each interior angle of the polygon
Given;
4.
[tex]x=108[/tex]
substituting into the formula and solving for n, we have;
[tex]\begin{gathered} x=\frac{(n-2)180}{n} \\ 108=\frac{(n-2)180}{n} \\ \text{cross multiply and expand;} \\ 108n=180n-360 \\ 180n-108n=360 \\ 72n=360 \\ n=\frac{360}{72} \\ n=5 \end{gathered}[/tex]
Therefore, the polygon has 5 sides;
[tex]n=5[/tex]
