Question 694996: how to find the measure of an interior angle and an exterior angle of a regular polygon with 16 sides Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! As you go around a polygon, at each vertex, you change direction by a certain angle as you "go around the corner". That angle is an exterior angle.
When you go all the way around a polygon with angles (and consequently sides), you have changed your direction by a whole turn around, a total of or .
If it was a regular polygon, all those exterior angles were congruent (same measure), and the measure of each was or
For a 16-sided regular polygon, the exterior angles measure or
The interior angle is the "corner" you turned around. It is the supplement of the exterior angle. The measures of the interior and exterior angles add up to OR .
In the case of your 16-sided regular polygon, the interior angles measure or
In general, the interior angle in a regular n-sided polygon measures or
