Interior Angle Sum

The sum of all the internal angles of a simple polygon is 180 n 2 where n is the number of sides.

Interior angle sum. Polygons interior angles theorem. The sum of exterior angles is 360. In a polygon of n sides the sum of the interior angles is equal to 2n 4 90.

Below is the proof for the polygon interior angle sum theorem. Find missing angles inside a triangle. Remember that a polygon must have at.

More lessons for grade 8 math worksheets examples solutions videos and worksheets to help grade 8 students learn about co interior angles also called consecutive interior angles same side interior angles. Interior angle sum of the interior angles of a polygon n. The polygon then is broken into several non overlapping triangles.

Since the interior angles add up to 180 every angle must be less than 180. When we start with a polygon with four or more than four sides we need to draw all the possible diagonals from one vertex. Sum of interior angles n 2 180 each angle of a regular polygon n 2 180 n.

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. Properties of interior angles. The other part of the formula n 2 step 2 count the number of sides in your polygon.

Sum of interior angles 360 how to find one interior angle to find the measure of a single interior angle then you simply take that total for all the angles and divide it by n the number of sides or angles in the regular polygon. Where n is the number of polygon sides. The interior angle is 180.