Sum Of The Interior Angles

It is easy to see that we can do this for any simple convex polygon.

Sum of the interior angles. Pick a point in its interior connect it to all its sides get n triangles and then subtract 360 from the total giving us the general formula for the sum of interior angles in a simple convex polygon having n sides as. This video demonstrates how to find the sum of the interior angles of any polygon. Specifically the sum of the angles is 180 1 4f where f is the fraction of the sphere s area which is enclosed by the triangle.

The video also makes the distinction between regular polygons and non regu. Number of sides 9 6 720. So the sum of the interior angles in the simple convex pentagon is 5 180 360 900 360 540.

3 sum of the interior angles 180. Angle sum of polygons as we know by angle sum property of triangle the sum of interior angles of a triangle is equal to 180 degrees. For a convex polygon with n sides we can divide it to n 2 triangles.

Browse more topics under lines and angles. Let us see the proof of this statement. The other part of the formula n 2 step 2 count the number of sides in your polygon.

Number of sides. The formula is sum n 2 180 displaystyle sum n 2 times 180 where sum displaystyle sum is the sum of the interior angles of the polygon and n displaystyle n equals the number of sides in the polygon 1 x research source the value 180 comes from how many degrees are in a triangle. The polygon then is broken into several non overlapping triangles.

Let n n equal the number of sides of whatever regular polygon you are studying. The sum of the interior angles of a triangle is 180 deg. When we start with a polygon with four or more than four sides we need to draw all the possible diagonals from one vertex.