# Each interior angle of a regular polygon is equal to 172 degrees. Determine the number of sides of the polygon. Explain?

May 15, 2016

$45$ sides
A regular polygon with $n$ sides has a total of $\left(n - 2\right) {180}^{o}$ internal degrees. This can be understood as the number of triangles in which the polygon can be decomposed.
A regular polygon with an interior angle of ${172}^{o}$ has a total of
$n {172}^{o}$. So we have
$n 172 = \left(n - 2\right) 180$. Solving for $n$ we have $n = 45$