Formula For The Interior Angles Of A Polygon

Each triangle has 180.

Formula for the interior angles of a polygon. Polygons are also classified as convex and concave polygons based on whether the interior angles are pointing inwards or outwards. Sum of interior angles of a three sided polygon can be calculated using the formula as. If the exterior angle of a polygon is given then the formula to find the interior angle is.

Interior angle of a polygon 180 exterior angle of a polygon. So in general this means that each time we add a side we add another 180 to the total as math is fun nicely states. S 180 n 2 this formula derives from the fact that if you draw diagonals from one vertex in the polygon the number of triangles formed will be 2 less than the number of sides.

If we know the sum of all the interior angles of a regular polygon we can obtain the interior angle by dividing the sum by the number of sides. Since we know that the sum of interior angles in a triangle is 180 and if we subdivide a polygon into triangles then the sum of the interior angles in a polygon is the number of created triangles times 180. An irregular pentagon and hexagon divided into triangles example sum.

So to calculate the sum of interior angles in a polygon you have to multiply the number of triangles in the polygon by 180. Sum of interior angles p 2 180 60 40 x 83 3 2 180 183 x 180 x 180 183. If n is the number of sides of a polygon then the formula is given below.