### Instruction: Each interior angle of a regular polygon measures $140^\circ$. How many sides does the polygon have?### Response: 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.