We have to find the measure of the interior angle of a regular polygon with 15 sides.
We can use the formula:
[tex]\alpha=\frac{(n-2)}{n}\cdot180\degree[/tex]where α is the interior angle and n is the number of sides of the polygon.
We can then calculate it as:
[tex]\begin{gathered} \alpha=\frac{15-2}{15}\cdot180\degree \\ \alpha=\frac{13}{15}\cdot180\degree \\ \alpha=156\degree \end{gathered}[/tex]Answer: 156 degrees.
