SOLUTION: You are given the measure of each interior angle of a regular n-gon. Find the value of n. a) 135 degrees b) 156 degrees c) 162 degrees d) 172 4/5 degrees

Algebra ->  Polygons -> SOLUTION: You are given the measure of each interior angle of a regular n-gon. Find the value of n. a) 135 degrees b) 156 degrees c) 162 degrees d) 172 4/5 degrees       Log On


   

Question 389431: You are given the measure of each interior angle of a regular n-gon. Find the value of n.
a) 135 degrees
b) 156 degrees
c) 162 degrees
d) 172 4/5 degrees
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We can solve this more quickly by finding the exterior angles of each n-gon. Note that the sum of the exterior angles in any convex polygon is 360 degrees. Given an interior angle, we can find the exterior angle by using 180 - x, where x is the interior angle measure.

Therefore, use the equation n+=+360%2F%28180+-+x%29 (substituting values for x) to find the value of n. For part a),

n+=+360%2F%28180+-+135%29+=+360%2F45+=+8, therefore it is an 8-sided polygon. Repeat for the other three measures.