SOLUTION: A polygon has an interior angle sum of 3060. How many sides must the polygon have?

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Question 1097500: A polygon has an interior angle sum of 3060. How many sides must the polygon have?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

By drawing all the diagonals from one vertex of a (convex) polygon with n sides, the polygon is divided into (n-2) triangles. The angle sum in each triangle is 180 degrees; and the sum of the interior angles of the polygon is the sum of all the angles in all the triangles.

(Draw a few figures of polygons with relatively small numbers of sides to see this, if it helps....)

So the sum of the angle measures of a convex polygon with n sides is 180%28n-2%29.

Your angle sum is 3060 degrees; 3060%2F180+=+17; so 17 is (n-2), which means the polygon has 19 sides.