Sum Of Interior And Exterior Angles Of A Polygon

For example an eight sided regular polygon an octagon has exterior angles that are 45 degrees each because 360 8 45.

Sum of interior and exterior angles of a polygon. 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. In any polygon the sum of an interior angle and its corresponding exterior angle is 180. Therefore the sum of exterior angles 360.

The angle next to an interior angle formed by extending the side of the polygon is the exterior angle. 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. X exterior angle 180 110 exterior angle 180 exterior angle 70 so the measure of each exterior angle corresponding to x in the above polygon is 70.

Here is the formula. 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. 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.

The sum of the measures of the interior angles of a polygon with n sides is n 2 180. 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.

In fact the sum of the interior angle plus the exterior angle of any polygon always add up to 180 degrees. Interior and exterior angle formulas. Interior angle adjacent exterior angle 180 degrees.

An exterior angle of a polygon is an angle outside the polygon formed by one of its sides and the extension of an adjacent side. The sum of the exterior angles of a regular polygon will always equal 360 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.