Each interior angle of a regular polygon measures $140^\circ$. How many sides does the polygon have?
I know that the sum of the interior angles of any polygon with $n$ sides is $(n-2)180^\circ$. So, if each angle is $140^\circ$, then the sum is $140n^\circ$. Setting these two expressions equal, I get $(n-2)180 = 140n$. Simplifying, I get $180n - 360 = 140n$, or $40n = 360$. Dividing by $40$, I get $n = 9$. So the polygon has $9$ sides. 