Question

What is the sum of the interior angles of the polygon shown below

Answer 1

Answer:

720 degrees.

Step-by-step explanation:

The sum of the interior angles of a convex polygon with  n  sides is

180(n - 2)  degrees.

In this case,  n = 6 sides, so the angle sum is

180(6 - 2) = 180(4) = 720 degrees.

The reason this works is that if you draw a diagonal from one vertex to the others (see attached image), you get 2 fewer triangles than the number of sides.  Each triangle contains a total of 180 degrees, so the total of all the interior angles is 180(n - 2).