Find the sum of the interior angles of a polygon with 20 sides?
maths question answer only or:maths question answer onlyor:If you put a straightedge on the outside of any figure and run it around, you can see that
maths question answer only
or:maths question answer only
or:If you put a straightedge on the outside of any figure and run it around, you can see that it makes exactly one complete revolution, proving that the sum of exterior angles of any figure, regular or irregular, is 360 degrees.The exterior angles average 360/20 = 18 degrees each, so the interior angles average 180 - 18 = 162 degrees each and the sum is 162 x 20 = 3240 degrees.
or:The sum of the interior angles of a triangle equals 180\u00b0. In a plane convex n-gon (Polygon with n sides and thus n corners) pick one corner. From this corner you can draw n-3 diagonals, thereby cutting it in n-2 triangles. The sum of the interior angles of that n-gon is then determined as the sum of 180\u00b0 times the number of these triangles:180 * (n - 2).Applying this consideration to a 20-gon yields:180\u00b0 * 18 = 3240\u00b0.
