The value 180 comes from how many degrees are in a triangle. The other part of the formula, n−2{\displaystyle n-2} is a way to determine how many triangles the polygon can be divided into. So, essentially the formula is calculating the degrees inside the triangles that make up the polygon. [3] X Research source This method will work whether you are working with a regular or irregular polygon. Regular and irregular polygons with the same number of sides will always have the same sum of interior angles, the difference only being that in a regular polygon, all interior angles have the same measurement. [4] X Research source In an irregular polygon, some of the angles will be smaller, some of the angles will be larger, but they will still add up to the same number of degrees that are in the regular shape.
For example, if you want to know the sum of the interior angles of a hexagon, you would count 6 sides.
For example, if you are working with a hexagon, n=6{\displaystyle n=6}, since a hexagon has 6 sides. So, your formula should look like this:sum=(6−2)×180{\displaystyle sum=(6-2)\times 180}
For example, to find out the sum of the interior angles of a hexagon, you would calculate:sum=(6−2)×180{\displaystyle sum=(6-2)\times 180}sum=(4)×180{\displaystyle sum=(4)\times 180}sum=(4)×180=720{\displaystyle sum=(4)\times 180=720}So, the sum of the interior angles of a hexagon is 720 degrees.
For example, you might want to find the sum of the interior angles of a hexagon, so you would draw a six-sided shape.
A vertex is a point where two sides of a polygon meet.
You do not have to draw lines to the adjacent vertices, since they are already connected by a side. For example, for a hexagon you should draw three lines, dividing the shape into 4 triangles.
For example, since you divided your hexagon into 4 triangles, you would calculate 4×180=720{\displaystyle 4\times 180=720} to find a total of 720 degrees in the interior of your polygon.
