Octagon
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A Hexagon has 3 pairs of parallel line and all angles are obtuse.
Some trapezoids have 2 acute angles, 2 obtuse angles, 1 pair of parallel lines, 1 short side, and 1 long side.
In two dimensions, lines can be parallel, angles cannot. So no plane shape has parallel angles.
parallelogram
A shape with no right angles and one pair of parallel lines would be called a trapezoid in the USA, and a trapezium in Britain.