Question 855465
An exterior angle is the angle you turn at each vertex as you go around the polygon:
{{{drawing(300,300,-6,4,-4,6,
line(0,0,0,-6),line(0,0,-4,6),
green(line(0,0,0,6)),red(arc(0,0,4,4,-126.9,-90)),
locate(-0.8,1.9,red(exterior)),
locate(-0.6,1.5,red(angle)),
locate(0.1,0.2,vertex),locate(-1.2,-2,side),
locate(-3,3,side),blue(arc(0,0,3.5,3.5,90,-126.9)),
locate(-2.3,0.2,blue(interior)),
locate(-1.4,-0.4,blue(angle))
)}}} The sum of the measures of all exteror angles is {{{360^o}}} .
An exterior angle is supplementary to the interior angle,
so if {{{x}}}= measure of each exterior angle in degrees,
{{{x+140}}}= measure of each interior angle in degrees,
and {{{x+(x+140)=180}}} .
 
Solving for {{{x}}} :
{{{x+(x+140)=180}}}
{{{(x+x)+140=180}}}
{{{2x+140=180}}}
{{{2x=180-140}}}
{{{2x=40}}}
{{{x=40/2}}}
{{{x=20}}}
 
If it is a regular polygon with {{{n}}} sides, it has {{{n}}} exterior angles,
each measuring {{{20^o}}} , and the sum of their measures (in degrees) is
{{{20n=360}}} --> {{{n=360/2}}} --> {{{highlight(n=18)}}}
The polygon has {{{highlight(18)}}} sides.