smc

The formula for the sum of the angles in any polygon is $180(n-2)$. Because this particular polygon is convex and has its angles in an arithmetic sequence with its largest angle being $160$, we can find the sum of the angles. $a_n=160$ $a_1=160-5(n-1)$ Plugging this into the formula for finding the sum of an arithmetic sequence... $n\left(\frac{160+160-5(n-1)}{2}\right)=180(n-2)$. Simplifying, we get $n^2+7n-144$. Since we want the positive solution to the quadratic, we can easily factor and find the answer is $n=\boxed{9}$. Hence the answer is$\boxed{9}$