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

For a.) you can use the equation for the sum of interior angles of a regular n-gon

(n - 2) * 180 degrees

For b.) you can divide this by the number of angles

What can you say about c.) and therefore d.) ?

Answer 2

a) 180*(n-2) =(2n-4)*90
b) 180 - 360/n
c) 360 (for all n sided polygons )
d) 360/n
e) 180