Question 798275
An interior angle of a polygon and the corresponding exterior angle are supplementary. They add up to {{{180^o}}}
{{{drawing(300,200,-3,3,-1,3,
line(-3,0,0,0),line(0,0,2.12,2.12),line(2.12,2.12,2.12,3),
blue(arrow(0,0,2.8,0)),green(arc(0,0,2,2,-45,0)),
locate(1,0.3,angle),locate(0.92,0.6,exterior),
red(arc(0,0,1.9,1.9,-180,-45)),locate(-0.45,0.5,red(135^o)),
locate(-1.5,1,angle),locate(-1.7,1.3,interior)
)}}} So the exterior angle measures {{{180^o-135^o=45^o}}}
 
EXTRA INFORMATION:
As you go around a polygon, an exterior angle is the change of direction as you "turn the corner". One whole turn around the polygon is {{{360^o}}}, so all the exterior angles add up to {{{360^o}}}.
In a regular polygon, all angles have the same measure, so after you turn your direction by {{{45^o}}} at {{{8}}} vertices, you will have made a complete
{{{8*45^o=360^o}}} turn around the polygon and will be going in the direction you started (and on the side you started).
That polygon has 8 vertices (and 8 sides). It's an octagon, just like a STOP sign.