# Math

• Given a polygon with 18 sides, find the sum of the measures of its interior angles.

A polygon with 18 sides has an interior angle measure sum of ______°. 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...

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

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