{"status": "success", "data": {"description_md": "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 $T_1, T_2, T_3,...,T_n$ returns the point $(1, 0)$ back to itself?\n\n$\\textbf{(A) } 359 \\qquad \\textbf{(B) } 360 \\qquad \\textbf{(C) } 719 \\qquad \\textbf{(D) } 720 \\qquad \\textbf{(E) } 721$", "description_html": "<p>Let  <span class=\"katex--inline\">T_k</span>  be the transformation of the coordinate plane that first rotates the plane  <span class=\"katex--inline\">k</span>  degrees counterclockwise around the origin and then reflects the plane across the  <span class=\"katex--inline\">y</span> -axis. What is the least positive integer  <span class=\"katex--inline\">n</span>  such that performing the sequence of transformations  <span class=\"katex--inline\">T_1, T_2, T_3,...,T_n</span>  returns the point  <span class=\"katex--inline\">(1, 0)</span>  back to itself?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 359 \\qquad \\textbf{(B) } 360 \\qquad \\textbf{(C) } 719 \\qquad \\textbf{(D) } 720 \\qquad \\textbf{(E) } 721</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2022 AMC 10A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10A_p19", "prev": "/problem/22_amc10A_p17"}}