Adjacent angles share a vertex and one ray, while any two angles that don't share both those things are nonadjacent.
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The line is called a diagonal if it is drawn between two nonadjacent angles.
A linear pair would be two angles that form a straight angle of 180 degrees.
Vertical
No. The non-vertical angles need not be related to one another in any way.
Adjacent. And if the adjacent angles are supplementary (add up to be 180o), then it's a linear pair.