Question

What is the angle sum of a polygon with 9 sides?

Answer 1

`1260˚`

Explanation:

A nonagon can have `6` diagonals drawn inside of it to form `7` interior triangles.

Every triangle's angles have a sum of `180˚`. Therefore, since there are `7` triangles, the sum of the interior angles in a nine-sided polygon is

`7xx180˚=1260˚`

This can be generalized to a polygon with `n` sides, since `n-2` triangles can be drawn in any polygon. Thus, the formula is

`180˚(n-2)`