The 45th parallel approximately defines most of the border between Montana and Wyoming in the United States. The 45th parallel approximately defines part of the international border between Quebec, Canada, and New York and Vermont, United States.
A 4-part "Ideas" radio program by the CBC (Canadian Broadcasting Corporation), called "On the Line: A Journal of Exploration along the Canada - U.S. Border" (presenter Marian Fraser), aired in Nov 1986 and used a series of interviews to tell the story of the border. Ep 2, "Survey and Surveillance" has a section about the Quebec/Vermont border.
Dr. Alec McEwan, [then] Canada's commissioner on the International Boundary Commission, explained how the border was established: The border between Lower Canada and New York was marked in the 1760s. That the line was off due to surveyor error was known at an early time. But Vermonters were sure it was already too far south and every arbitration attempt (1790s, 1814, 1830s) to correct the survey error was stymied.
So the boundary was not settled there until 1842. The Webster-Ashburton Treaty established the line, or kept the line where it had always been, along the old so-called Valentine Collins line, along the demarcated line, approximately a mile north of the true 45th parallel, which kept the fort [Fort Montgomery, at Rouse Point] in the United States.