Interior Angle Formula

Sum of interior angles n 2 180 each angle of a regular polygon n 2 180 n.

Interior angle formula. Sum of interior angles p 2 180 60 40 x 83 3 2 180 183 x 180 x 180 183. The formula can be proved using mathematical induction and starting with a triangle for which the angle sum is 180 then replacing one side with two sides connected at a vertex and so on. Below is the proof for the polygon interior angle sum theorem.

The sum of the measures of the interior angles of a polygon with n sides is n 2 180. The measure of each interior angle of an equiangular n gon is if you count one exterior angle at each vertex the sum of the measures of the exterior angles of a polygon is always 360. Interior angle sum of the interior angles of a polygon n.

If you prefer a formula subtract the interior angle from 180. E x t e r i o r a n g l e 180 i n t e r i o r a n g l e exterior angles examples. Interior and exterior angle formulas.

S n 2 180 s 8 2 180 s 6 180 s 1 080 next divide that sum by the number of sides. Polygons interior angles theorem. The sum of the internal angle and the external angle on the same vertex is 180.

The sum of the interior angles 2n 4 right angles. An interior angle is located within the boundary of a polygon. The sum of all of the interior angles can be found using the formula s n 2 180.

The formula is where is the sum of the interior angles of the polygon and equals the number of sides in the polygon. Here is an octagon eight sides eight interior angles. Polygons are also classified as convex and concave polygons based on whether the interior angles are pointing inwards or outwards.