SOLUTION: The measure of each exterior angle of a regular n-gon is 18°. A) Find the value of n. B) What is the measure of each interior angle?

Algebra ->  Polygons -> SOLUTION: The measure of each exterior angle of a regular n-gon is 18°. A) Find the value of n. B) What is the measure of each interior angle?      Log On


   



Question 1178667: The measure of each exterior angle of a regular n-gon is 18°.
A) Find the value of n.
B) What is the measure of each interior angle?

Found 3 solutions by ikleyn, MathLover1, Alan3354:
Answer by ikleyn(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.

The sum of exterior angles of any convex polygon is 360 degrees.


Therefore, in the given case, the number of vertices n is equal to  360%2F18 = 20.


The measure of the interior angle is  180-18 = 162 degrees.



Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The measure of each exterior angle of a regular n-gon is 18°.
A) Find the value of n.
The sum of the n exterior angles for any convex polygon with n sides is 360 degrees.
18n=360
n=360%2F18
n=20
B) What is the measure of each interior angle?
The measure of each angle in a regular n-gon is
m < =+%28n-2%29180%2Fn˚.......n=20
m < =+%2820-2%29180%2F20˚
m < =+162˚

Answer by Alan3354(69443) About Me  (Show Source):