# 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? Hello!

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.

Approved by eNotes Editorial Team 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.

Approved by eNotes Editorial Team