SOLUTION: the ratio of the interior angles and exterior angles of a regular n-gon (n sided polygon) to the exterior angles is 10 to 2, what is the measure of each interior angle and exterio

You are given that the ratio of the interior angle of the regular n-gon to its exterior angle is 10:2, i.e, 5:1.


From the other side, the sum of these angles is 180 degrees, as you should know.


Hence, the exterior angle is   =  = 30 degrees.


Then the interior angle is  180-30 = 150 degrees, obviously.



From the other side, the sum of the exterior angles of any n-sided convex polygon is 360 degrees.


It gives you an equation


    n*30 = 360  degrees


to find the number of sides / (of vertices) of the polygon.


From the equation, you easily find  n =  = 12.


ANSWER.  The given polygon is 12-gon.