smc

Let $n$ equal the number of sides the polygon has. The sum of all the interior angles of a polygon is: $180(n-2)$. The formula for an arithmetic series is $\frac{n(a_1+a_n)}{2}$. Set this equal to $180(n-2)$ and solve. In this case, $a_1=100$ and $a_n=140$. Our equation becomes $\frac{n(100+140)}{2}=180(n-2)\Rightarrow 240n=360(n-2)\Rightarrow 120n=720$. Simplifying, we get $n=\boxed{6}$