Question

prove that sum of the measure of the external angles of any polygon is 360​

Answer 1

Answer:

The sum of interior angles of a regular polygon with n sides is 180 (n-2).

so, each interior angle has measure 180 (n-2)/n.

each exterior angle is the supplement to an interior angle .

so , the measure of exterior angle is:

180-180 (n-2)/n = [180n-180n + 360] /n = 360/n

sum of exterior angles = n (360/n) =360 ,

hence proved.