Assume the exterior angle of the polygon is denoted as x, leading to the interior angle being 120+x. Applying the property that the sum of interior and exterior angles in a polygon is always 180∘180∘, we set up the equation x+(120+x)=180, simplifying to 2+120=1802x+120=180. Solving for x, we find x=30∘.
With the exterior angle established as 30∘, consider a polygon with n sides. The total sum of exterior angles in any polygon is always 360∘, so n×x=360 becomes n×30=360. Solving for n, we find n=12.
Therefore, the polygon in question has 12 sides.
Let exterior angle is
Interior angle will be
interior angle exterior angle
so
degree. Exterior angle .
Let there are sides so
so there are sides of polygon.