Question

** ** In a regular polygon, each interior angle is 120 more than each exterior angle. Find the number of diagonals of the polygon.

Answer 1

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=1802 x +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.