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For a regular n-gon:

AWhat is the sum of the measures of its angles?
BWhat is the measure of each angle?
CWhat is the sum of the measures of its exterior angles, one at each vertex?
DWhat is the measure of each exterior angle?
EFind the sum of your answers to parts b and d. Explain why this sum makes sense.

Verified Answer :

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

HomertheGenius

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°

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