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Infinitely many. Polygons with 6 or more sides can have 3 pairs of parallel lines. Polygons with 7 or more sides can have a set of three parallel lines.
You can have 0, 1, 2, or 3 pairs of parallel sides in a heptagon.
There are 3 pairs of parallel sides. All 6 sides are parallel to 1 other side.
Angle
A parallogram has two pairs of parallel sides. A trapezoid has one pair of parallel sides. A regular octagon has four pairs of parallel sides. An irregular octagon may have from 3 pair to no pair of parallel sides.