Strictly speaking you cannot have one parallel side - you must have one pair.
Any irregular polygon with four or more sides can have a pair of parallel sides. Most have no specific names - the only one that does is a trapezium.
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A quadrilateral in the shape of a kite has no parallel sides
Any shape wit four of more sides can have one pair of parallel sides.
A trapezoid has exactly one pair of parallel sides
trapezoid
A trapezoid has only one pair of parallel sides