Polygon Interior Angle Sum

Each interior angle of a regular polygon measures 160.

Polygon interior angle sum. In a regular polygon all the interior angles measure the same and hence can be obtained by dividing the sum of the interior angles by the number of sides. Hence we can say now if a convex polygon has n sides then the sum of its interior angle is given by the following formula. The angle sum of this polygon for interior angles can be determined on multiplying the number of triangles by 180.

Same thing for an octagon we take the 900 from before and add another 180 or another triangle getting us 1 080 degrees. So you would use the formula n 2 x 180 where n is the number of sides in the polygon. After examining we can see that the number of triangles is two less than the number of sides always.

So we can use this pattern to find the sum of interior angle degrees for even 1 000 sided polygons. In order to find the measure of a single interior angle of a regular polygon a polygon with sides of equal length and angles of equal measure with n sides we calculate the sum interior angles or n 2 180 and then divide that sum by the number of sides or n. In any polygon the sum of an interior angle and its corresponding exterior angle is 180.

This gives us the formula total interior angles n 2 180 where n is the number of sides. Sum of interior angles n 2 180 each angle of a regular polygon n 2 180 n. How many sides does the polygon have.

S n 2 180. Sum of interior angles p 2 180. A heptagon has 7 sides so we take the hexagon s sum of interior angles and add 180 to it getting us 720 180 900 degrees.

Sum of all the interior angles of a polygon is equal to the product of a straight angle and two less than the number of sides of the polygon. To determine the total sum of the interior angles you need to multiply the number of triangles that form the shape by 180. Interior angles sum of polygons.