HMMT 2006 T9

Let $n \geq 3$ be a positive integer. Prove that given any $n$ angles $0<\theta_{1}, \theta_{2}, \ldots, \theta_{n}<$ $180^{\circ}$, such that their sum is $180(n-2)$ degrees, there exists a convex $n$-gon having exactly those angles, in that order.