Question

The instructions say, "The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle. Then find the number of sides. For another problem just like this, they gave the number 18 and I subtracted 18 from 180 and solved it like this, 162n=(n-2)180. However in this case they gave the variable x. How do I find what the number is instead of x so I can solve my problem?

Answer 1

In the actual case they had 18°
So in the general case they now have x°

So let's do exactly the same thing
So if we have n sides and the exterior angle is x°
then the interior angle is 180-x

So (180-x)n = (180)(n-2)
180x - nx = 180n + 360

solving for n:

180x - 360 = 180n + nx
180x - 360 = n(180-x)
n = (180x - 360)/(180-x) ---> number of sides

solving for x:
x(180 - n) = 180n + 360
x = (180n + 360)/(180 - n)