Question 1150931
.
<pre>

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  {{{180/(5+1)}}} = {{{180/6}}} = 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 = {{{360/30}}} = 12.


<U>ANSWER</U>.  The given polygon is 12-gon.
</pre>

From this point, complete the solution on your own.


--------------


Do not forget to post your "THANKS" to me for my lesson (!)