An isosceles trapezoid would seem to fit the given description.
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
A shape that has 4 right angles and 2 pairs of parallel lines is a rectangle. In a rectangle, all four angles are right angles, meaning they measure 90 degrees each. Additionally, opposite sides of a rectangle are parallel, resulting in two pairs of parallel lines within the shape.
In two dimensions, lines can be parallel, angles cannot. So no plane shape has parallel angles.
a square
trapizoid
A rhombus
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.
Parallelogram
A Trapizoid.
A shape that has two parallel lines and no perpendicular lines is a trapezoid, specifically an isosceles trapezoid. In this shape, one pair of opposite sides is parallel, while the other pair is not perpendicular to the parallel sides. This creates a unique geometry without right angles. Another example could be a parallelogram, which also has two pairs of parallel sides but does not necessarily have any perpendicular lines.
A parallelogram.
The shape you are describing is a rectangle. In a rectangle, there are two pairs of parallel sides, and opposite sides are equal in length. Additionally, the opposite angles are equal, with each angle measuring 90 degrees. A square is a specific type of rectangle where all sides are equal in length.