A polygon with 4 or more sides can have a pair of parallel sides.
quadrilateral
rhombus
A trapezoid.
For a 4-sided polygon (a quadrilateral), the shape is a trapezoid (trapezium in the UK).*The question was copied in and omitted the "4 sided" restriction. There are innumerable irregular polygons that have a single pair of parallel sides, those that have 5 or more sides.
An irregular quadrilateral, though it could possibly be a kite if there are two pairs of sides of equal length
I am a quadrilateral, I have 4 vertices, I only have one pair of parallel sides, and I am also a polygon. What am I?
Any polygon with 4 or more sides can have 2 parallel sides.
Any irregular polygon with 4 or more sides can have only one pair of parallel sides. For example, a child's drawing of the silhouette of a house (the base, two walls and a triangular roof) is a pentagon and the two walls are the 1 pair of parallel sides.
trapazoid
quadrilateral
There are two pairs of parallel sides in a rectangle - 1 pair of lengths, and 1 pair of widths.Therefore, 4 parallel sides!