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and when it is regular all angles the same then each angle is 540 5 108 exercise make sure each triangle here adds up to 180 and check that the pentagons interior angles add up to 540 the interior angles of a pentagon add up to 540, video transcript and then i just have to multiply the number of triangles times 180 degrees to figure out what are the sum of the interior angles of that polygon so lets figure out the number of triangles as a function of the number of sides so once again four of the sides are going to be used to make two triangles, sum of interior angles for example the interior angles of a pentagon always add up to 540 no matter if it regular or irregular convex or concave or what size and shape it is the sum of the interior angles of a polygon is given by the formula sum 180 n 2 degrees where n is the number of sides, interior and exterior angle formulas the sum of the measures of the interior angles of a polygon with n sides is n 2180 the measure of each interior angle of an equiangular ngon 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
set up the formula for finding the sum of the interior angles the formula is sumn2180displaystyle sumn2times 180 where sumdisplaystyle sum is the sum of the interior angles of the polygon and ndisplaystyle n equals the number of sides in the polygon the value 180 comes from how many degrees are in a triangle, an interior angle of a polygon is an angle inside the polygon at one of its vertices exterior angle 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
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find the sum of interior angles of different polygons if youre seeing this message it means were having trouble loading external resources on our website if youre behind a web filter please make sure that the domains kastaticorg and kasandboxorg are unblocked, 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 anglesor red n2 cdot 180 and then divide that sum by the number of sides or red n, sum of interior angles 360 n x 180 sum of interior angles n x 180 360 n2 x 180 method 6 this method needs some knowledge of difference equation it is a bit difficult but i think you are smart enough to master it let x n be the sum of interior angles of a nsided polygon so you may say that x n1 is the sum of , showing a generalized way to find the sum of the interior angles of any polygon practice this lesson yourself on right now httpswwwkhanacademy