The Interior Angle Equation of a Polygon

Here is an example of how the equation used to find the interior angle measure sum in polygons works.

Angle sum = (n-2)(180)

This is a Lamborghini that I photographed at a car show. Notice how the headlights form pentagons. Now we will test to see if the equation works.

To find the sum of the interior angles in a pentagon, the equation is (5-2)(180).

(5 - 2)(180)
= 3(180)
= 540

So, the total measure of all the angles in a pentagon equals 540 degrees. This equation should work for all pentagons, so now let's test to see if it works on the headlight.

As we can see, the measures of all the angles are: 54.56, 129.09, 103.2, 136.76, and 116.39. If we add these all together, we get 540, which proves the equation to be correct, for both regular and non-regular polygons. (~DM5)