Well it could be complementary or supplementary because they don't have to share a vertex yet I think you mean something like the vertical angle. You can go research vertical angles. I'll give you a link for the vertical angles.
http://www.mathsisfun.com/geometry/vertical-angles.html
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Yes, since the vertex is a point and the vertical angles share that point.
adjacent angles
opposite angles
Adjacent angles share a vertex and one ray, while any two angles that don't share both those things are nonadjacent.
An adjacent angle