Sum Of Interior And Exterior Angles Of A Polygon

Interior and exterior angle formulas.

Sum of interior and exterior angles of a polygon. Here is the formula. The sum of the measures of the interior angles of a polygon with n sides is n 2 180. Hence we can say if a polygon is convex then the sum of the degree measures of the exterior angles one at each vertex is 360.

The angle next to an interior angle formed by extending the side of the polygon is the exterior angle. That is interior angle exterior angle 180 then we have. The sum of interior angles in a quadrilateral is 360º a pentagon five sided polygon can be divided into three triangles.

For example an eight sided regular polygon an octagon has exterior angles that are 45 degrees each because 360 8 45. This is so because when you extend any side of a polygon what you are really doing is extending a straight line and a straight line is always equal to 180 degrees. Formula to find the sum of interior angles of a n sided polygon is n 2 180 by using the formula sum of the interior angles of the above polygon is 6 2 180.

Therefore the sum of exterior angles 360. The sum of exterior angles of any polygon is 360º. Let n n equal the number of sides of whatever regular polygon you are studying.

Interior angle adjacent exterior angle 180 degrees. Sum of the interior angles of a polygon 180 n 2 degrees interior angles of a polygon formula the interior angles of a polygon always lie inside the polygon. The sum of the exterior angles of a regular polygon will always equal 360 degrees.

Sum of interior angles n 2 180 s u m o f i n t e r i o r a n g l e s n 2 180. The sum of its angles will be 180 3 540 the sum of interior angles in a pentagon is 540. The formula for the sum of that polygon s interior angles is refreshingly simple.