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Polygons
Polygon Angle Sum

If the polygon has n sides, the sum, S, of the degree measures of these n interior angles is given by the formula:

S=(n-2)x180º

By joining one vertex of a polygon to every other vertex, (except the two it already adjoins), the polygon will be divided into a number of triangles. The number of triangles will always be 2 less than the number of sides of the polygon. Because the angle sum of a triangle sum is 180º, the angle sum of a polygon with n sides will be (n-2)x180º.

 Polygon Number of sides Number of triangles Sum of Angle Measure Triangle 3 1 1·(180º)=180º Quadrilateral 4 2 2·(180º)=360º Pentagon 5 3 3·(180º)=540º Hexagon 6 4 4·(180º)=720º

Find the sum of the angles of a dodecagon.

n=12
angle sum=(n-2)·180º=(12-2)·180º=10·180º=1800º

If the angle sum in a polygon is 1440º, how many sides does it have?

angle sum = (n-2)·180
1440 = (n-2)·180
1440 = 180n - 360
1800=180n
n=10
It is a decagon.