Question

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

Answer 1

`45` sides

Explanation:

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`