Polygon opposite sides

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It might help to know the context in which you have seen the phrase;
but I would say that, in a polygon with an even number of edges, the
side opposite a given side is the side that is separated from that
side by the same number of sides in each direction. Perpendicularity
or convexity is not required, only an even number of edges. You could
define it a bit more formally by saying that, for a 2n-gon, more examples on help in math;
the
opposite side is the nth side counting from the given side in either
direction.

In a pentagon, there is a vertex opposite each side, but not a side
opposite a side.