AMC 12 2022a Problem 18

Let $T_k$ be the transformation of the coordinate plane that first rotates the plane $k$ degrees counterclockwise around the origin and then reflects the plane across the $y$-axis. What is the least positive integer $n$ such that performing the sequence of transformations $T_1, T_2, T_3, \dots, T_n$ returns the point $(1,0)$ back to itself?

$\textbf{(A) } 359 \textbf{(B) } 360 \textbf{(C) } 719 \textbf{(D) } 720 \textbf{(E) } 721$