Question

Do you use the formula:
(n-2)180 / n
to find the measure of each arc that corresponds to a side of a polygon? Example: a hexagon
(6-2))180/6 = 120 ?

Answer 1

Nope. 360/n corresponds to the arc subtended by each side: the central angle.

The sum of the interior angles is (n-2)*180

So, (n-2)180/n is the measure of each interior angle of the polygon.

Note that
180(n-2)/n = (180n-360)/n
= 180 - 360/n
This shows that the central angle is equal to the exterior angle. (The interior and exterior angles are supplementary.)

Answer 2

Let me explain. The formula (n-2)x180 is used for getting the sum of all the interior angles of a polygon and the formula (n-2)x180/n is used for getting the measure of each angle