polygon angles

this dissection suggests a rule that might be easier to appreciate than drawing diagonals from one corner

it is also the method that Euclid appears to have chosen (as a corollary to the angles in a triangle summing to 180 degrees)

the angle sum for an 'n' sided polygon is
n x 180 - 360 

at each vertex the interior angle + exterior angle  = 180

if there are 'n' sides then the sum of the exterior angles plus the interior angles = 180n

as the sum of the interior angles is (n - 2) x 180 so the sum of the exteriors must be 360 to make the total of 180n