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Lesson 126: Sum of Interior Angles of Polygons
In this quick and easy lesson we'll learn a simple formula to find the sum of the interior angles of any polygon.
We learned in a previous lesson that the sum of the interior angles in any triangle is 180°. The sum of the interior angles in any quadrilateral (four-sided figure) is 360°. A pentagon (5 sides) has interior angles which add to 540°. The pattern is that we add 180° for every side that we add to our shape.
There is a simple formula that we can use to find the sum of the angles in a shape with n sides. The formula is (n - 2)180. That means that we subtract two from the number of sides, and multiply by 180.
It's easy to forget this formula, since it doesn't come up all that often. If you do, it's very easy to remind yourself of what it is, as long as you remember the number of degrees in a triangle and quadrilateral. Once you remember those numbers, you'll see that all you need to do is subtract 2 from the number of sides, and multiply by 180 to get the sum of the interior angles in the shape.
There is another important definition that you should know. A regular polygon is one in which all of the sides are equal. For example, a stop sign is a regular octagon. The formula above works whether the polygon is regular or not.
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