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

##45## sides

A regular polygon with ##n## sides has a total of ##(n-2)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 = (n-2)180##. Solving for ##n## we have ##n = 45##