Claire adds the degree measures of the interior angles of a convex polygon and arrives at a sum of $3017$. She then discovers that she forgot to include one angle. What is the degree measure of the forgotten angle?

Need $0<180(n-2)-3017<180$.

$180(n-2)>3017\Rightarrow n\ge19$. For $n=19$: $180(17)-3017=3060-3017=43$, valid.

For $n=20$: $180(18)-3017=3240-3017=223>180$, invalid. So the forgotten angle is $\boxed{43}$.