Question 163744
Let x=measure of exterior angle and y = measure of interior angle


We know that the formula for the interior angle is {{{interior_angle=180(n-2)/n}}} 


So in this case {{{y=180(n-2)/n}}} 


Also, remember that  {{{x+y=180}}} since the sum of the interior and exterior angle is 180


{{{y=180-x}}}  Solve for "y"



{{{180(n-2)/n=180-x}}} Plug in  {{{y=180(n-2)/n}}}



{{{180(n-2)=180n-xn}}} Multiply EVERY term by "n" to clear the fraction



{{{180n-360=180n-xn}}} Distribute



{{{-360=-xn}}} Subtract 180n from both sides. 



{{{-360/(-n)=x}}} Divide both sides by -n  to isolate x (which is the exterior angle)



{{{x=360/n}}} Reduce



So this shows that for any regular n-gon, the exterior angle will be {{{360/n}}}