Question

For a regular n-gon:

a. What is the sum of the measures of its angles?
b. What is the measure of each angle?
c. What is the sum of the measures of its exterior angles, one at each vertex?
d. What is the measure of each exterior angle?
e. Find the sum of your answers to parts b and d. Explain why this sum makes sense.

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°