Question

the exterior angle of a regular polygon is equal to one third of the interior angle. calculate the number of sides of the polygon and give its name

Answer 1

The angle in a regular polygon is ((n-2)*180)/n with n being the number of sides. The exterior angles would be (360)/n since exterior angles add up to 360. Therefore, (360)/n= (((n-2)*180)/n)*1/3. Multiplying both sides by n, we get 360=((n-2)*180)*1/3. After that, we divide both sides by 180 and multiply both sides by 3 to get 6=n-2. Therefore, n=8 and it is an octagon