What is the sum of an angle of a 20-gon?

Answer 1

The 20-gon has 20 sides and 20 vertices. Let's pick a point approximately in the center. Join each vertex to this point. Do you see twenty triangles now? The sum of the angles in a triangle is 180 degrees. So the total of all the angles in the twenty triangles is 20 x 180 but this includes all the angles around the point you selected and to which you joined the vertices. These angles (believe or not) form a circle with a total angle of 360 degrees. This you have to take away from 20 x 180 obtained before. So the sum of the internal angles of a 20-gon is 20 x 180 -360 which is 3240 degrees or 36 x 90 degrees. The general formula for the sum of the internal angles of a plane two dimensional closed n-sided polygon is

(2n - 4) x rightangles, where a rightangle is 90 degrees