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Infinitely many. Every regular polygon with 2n sides has n pairs of parallel sides. Then there are irregular polygons which can have parallel sides. And there are also irregular shapes which have parallel sides.
Their are 4 pairs of parallel sides on an octagon. In fact, for any regular polygon with an even number of sides, there will be # of sides / 2 number of pairs of parallel lines.
The number of pairs of parallel sides in a polygon varies depending on the type of polygon. For example, a rectangle has two pairs of parallel sides, while a trapezoid has one pair. Regular polygons, like a hexagon, typically do not have any pairs of parallel sides. Therefore, the total can range from zero to multiple pairs, depending on the specific polygon in question.
It depends on the base. If the base is an n-sided regular polygon, the pyramid will have n/2 pairs of parallel sides. The number of parallel sides when the base is irregular will depend on the exact details of the base.