Question

The interior angle of a polygon is 6 times it's exterior angle. Find the number of sides and the sum of all the interior angle. What is the name of the polygon

Answer 1

Solution:
Let the exterior angle be x,
then interior angle =6x
Sum of interior and exterior angle=180
x+6x=180
7x=180
x=180/7
So exterior angle=180/7
Interior angle=6x=6*180/7=1080/7
Number of sides=360/exterior angle=360/(180/7) = 2*7 = 14
Sum of interior angles=(n-2)180=(14-2)180=12*180= 2160 degrees.
Polygon = 14-gon