Question 550746: Find the number of sides of a convex polygon if the measures of its interior angles have a sum of 6840° Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! The sum of the measures of the interior angles of a convex polygon with n sides is (n-2)180°.
An easy way to understand and remember that is imagining a point in the interior of the polygon connected to all of the vertices forming n triangles.
The sum of all the angles in those triangles would be n(180°).
If you subtract the 2(180°)=360° corresponding to the angles at the point inside the polygon, you get the sum of the measures of the interior angles as (n-2)180°.
6840°/180°=38=n-2 --> n=40
The number of sides of that polygon is 40.
I am not going to draw it.
