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

Mathematics

1 answer:

DanielleElmas [232]1 year ago

7 0

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).

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