Question

The measure of an interior angle of a regular polygon is 140. Find the number of sides the polygon has.

Answer 1

(n-2)180=sum of the interior angles. If you just want to find one angle, then you divide (n-2)180 by the number of sides and you get
= one angle of a regular polygon
since you know the angle, you set the angle equal to
Let the angle be represented by A.
using algebra, we can say

180n-360-An=0
180n-An=360
n(180-A)=360
n=360/(180-A)
Therefore, the formula to find out the number of sides of a regular polygon when one interior angle is given is:

Where n=number of sides and A is the given angle.