Final answer:
The boundary west of Montana is a convergent boundary where the Juan de Fuca Plate is being subducted under the North American Plate, forming the Cascade Range and causing deep earthquakes.
Step-by-step explanation:
The type of plate boundary directly west and adjacent to the plate on which Montana is located is a convergent boundary. This particular boundary is where the Juan de Fuca Plate is being subducted beneath the North American Plate along the Pacific Northwest coast.
The tectonic processes associated with this convergent boundary have formed the Cascade Range, including volcanoes like Mt. St. Helens, due to the subduction of the Juan de Fuca Plate beneath the North American Plate. Subduction zones like this one are also responsible for deep earthquakes and the creation of volcanic mountain chains.