What is the sum of the measures of the interior angles of a polygon with 18 sides?

Given a polygon with 18 sides, what is the sum of the measures of its interior angles? 

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The answer is 180°*16 = 2880°.

The general formula is Sa=180°*(n-2) for any polygon with n sides.

This formula may be proved relatively easy for convex polygons. Consider a point P in the interior of the polygon and draw segments from this point to all vertices.

We obtain n triangles, each has the sum of angles 180°. The sum of angles whose vertex isn't P is the sum of interior angles of the polygon. The sum of angles whose vertex IS P is one complete circle, i.e. 360°.

So we have 180°*n=Sa+360°, or Sa=180°*(n-2).

This theorem holds for concave polygons also but the proof is more difficult.

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The sum of the measures of the interior angle of any polygon is the number of sides minus 2 multiplied by 180.

`S=(n-2)*180`

`S=(18-2)(180)`

S=16(180)

S=2880

A polygon with 18 sides has an interior angle sum of 2880 degrees.

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