Final answer:
The best name for angle Y in triangle XYZ is a remote interior angle. None of the other options correctly describe an angle within the triangle relative to another angle or side of the triangle.
Step-by-step explanation:
The best name for angle Y in triangle XYZ is a remote interior angle. An exterior angle of a triangle is the angle formed by one side of the triangle and the extension of an adjacent side. An alternate interior angle would be an angle on the opposite side of a transversal that cuts across two lines but inside the space between the lines. An adjacent interior angle is the angle that is adjacent (next to) another interior angle on the same side of the transversal but not the one we are naming. Therefore, the correct choice is C. Remote interior angle because it refers to the interior angles of a triangle that are not adjacent to the exterior angle being considered. We do not use cosine or components of vectors specifically to name this angle.