Question

For a regular n-gon:

Answer 1

180(n-2)/n 
=B + D 
= 180(n-2)/n + 360/n 
=180(n-2)/n + 180(2)/n 
=180(n-2+2)/n 
=180 
 measure of the interior angle + the measure of the exterior angle is 180
Because the combination of both angles, is a straight line.

b. What is the measure of each angle
hope this helps

Answer 2

A ) S n = ( n - 2 ) · 180°
b ) The measure of each angle:
α = ( n -2 ) · 180° / n
c ) Sum of all exterior angles: 360°
d ) The measure of each exterior angle:
α 1 = 360° / n
e ) ( n - 2 ) · 180° / n  + 360° / n = 
= ( 180° n - 360° + 360° ) / n = 180° n / n = 180° 
It makes sense because:
α (interior angle)+ α 1 ( exterior angle ) = 180°