Finding the measure of an individual interior angle in any regular polygon

When finding the measure of an interior angle in any regular n-gon (n means any number), triangles are very helpful. As you can see in the left most diagram, a regular pentagon has been split into 3 triangles so 5-2=3 or n-2. In the regular hexagon on he right there are 4 triangles 6-2=4 or n-2. So to find the number of triangles is easy, it's n-2.

Hopefully you already know that the area of a triangle is 180 and since each corner of the triangle is a vertice in the polygon, we no that the sum of all interrior angles in the regular n-gon is the number of triangles x 180 so the number of triangles is (n-2) and so our forumla so far is 180(n-2)

Since we know that in any regular n-gon, all angles are the same measure, we can just divide the sum of all angles by the number of angles. So our final forumla to find the measure of any angle in a regular n-gon is 180(n-2)/n

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