Claire adds the degree measures of the interior angles of a convex polygon and arrives at a sum of $2017$. She then discovers that she forgot to include one angle. What is the degree measure of the forgotten angle? $\textbf{(A)}\ 37\qquad$ $\textbf{(B)}\ 63\qquad$ $\textbf{(C)}\ 117\qquad$ $\textbf{(D)}\ 143\qquad$ $\textbf{(E)}\ 163$
Solution
The true sum of interior angles of a convex $n$-gon is $180(n-2)$, and the forgotten angle satisfies $0<180(n-2)-2017<180$.
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?
