2022 AMC 12A Problems/Problem 18

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Problem

Let $T_k$ be the transformation of the coordinate plane that first rotates the plane $k$ degrees counter-clockwise 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 $T_1, T_2, T_3, \cdots, T_n$ returns the point $(1,0)$ back to itself?

Solution

https://youtu.be/QQrsKTErJn8

(Professor Chen Education Palace, www.professorchenedu.com)