Question 19
We say a nondegenerate triangle whose angles have measures $\theta_1, \theta_2, \theta_3$ is *quirky* if there exists integers $r_1, r_2, r_3$, not all zero, such that
$$
r_1\theta_1 + r_2\theta_2 + r_3\theta_3 = 0.
$$
Find all integers $n \ge 3$ for which a triangle with side lengths $n-1, n, n+1$ is quirky.
$$
r_1\theta_1 + r_2\theta_2 + r_3\theta_3 = 0.
$$
Find all integers $n \ge 3$ for which a triangle with side lengths $n-1, n, n+1$ is quirky.