Question 997712
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Let  x  be the measure of the interior angle in degrees.

then the exterior angle is  {{{x/3}}}  and their sum is 


{{{x }}} + {{{x/3}}} = 180°.


Hence,  x = {{{(3*180)/4}}} = 135°.


The sum of interior angles is n*135°.

From the other side, it is (n-2)*180.


So, we have an equation 


(n-2)*180 = n*135.


Divide both sides by 45. You will get


(n-2)*4 = n*3, or 


4n - 8 = 3n,


4n - 3n = 8,


n = 8.


Our polygon is octagon.