Question 694996
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.
{{{drawing(200,200,-5,5,-5,5,
arrow(1,-5,1,-2), line(1,-2,1,0),
arrow(1,0,-2,3),line(-2,3,-4,5),
green(arrow(1,0,1,3)),green(line(1,3,1,5)),
locate(-2.3,4,exterior),locate(-1.2,3,angle),
locate(-3.5,1,interior),locate(-2,0,angle)
)}}}
When you go all the way around a polygon with {{{n}}} angles (and consequently {{{n}}} sides), you have changed your direction by a whole turn around, a total of {{{360^o}}} or {{{2pi}}}.
If it was a regular polygon, all those exterior angles were congruent (same measure), and the measure of each was {{{360^o/n}}} or {{{2pi/n}}}
For a 16-sided regular polygon, the exterior angles measure
{{{360^o/16=highlight(22.5^o)}}} or {{{2pi/16=highlight(pi/8)}}}
 
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 {{{180^o}}} OR {{{pi}}}.
In the case of your 16-sided regular polygon, the interior angles measure
{{{180^o-22.5^o=highlight(157.5^o)}}} or {{{pi-pi/8=highlight(7pi/8)}}}
 
In general, the interior angle in a regular n-sided polygon measures
{{{180^o-360^o/n=n*180^o/n-2*180^o/n=(n-2)180^o/n}}} or {{{pi-2pi/n=n*pi/n-2pi/n=(n-2)pi/n}}}