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

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#### Explanation:

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13
Nov 3, 2016

$45$ sides

#### Explanation:

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 $n = 45$

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