An isosceles trapezoid would seem to fit the given description.
The shape you are describing is called a trapezoid. It has two parallel sides, two parallel angles, and only one pair of opposite sides is parallel.
square
In two dimensions, lines can be parallel, angles cannot. So no plane shape has parallel angles.
a square
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.
A Trapizoid.
square
In two dimensions, lines can be parallel, angles cannot. So no plane shape has parallel angles.
a square
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.
trapizoid
A rhombus
Parallelogram
A Trapizoid.
A parallelogram.
The rhombus.
None
Octagon