The quadrilaterals that have two pairs of opposite sides that are parallel and no right angles are known as parallelograms, specifically rectangles and rhombuses. However, rectangles contain right angles, so the focus is primarily on rhombuses and general parallelograms that do not conform to right angles.
A rhombus is a type of parallelogram where all four sides are of equal length, but the angles are not necessarily 90 degrees. Typically, rhombuses have two acute angles and two obtuse angles, thus fulfilling the requirement of having no right angles.
Another example is a general parallelogram in which opposite sides are parallel and of equal length, but again, it can be structured in such a way that none of the internal angles are right angles. This means that while every parallelogram has pairs of parallel sides, only those that specifically lack right angles fit our criteria.
In summary, the quadrilaterals with two pairs of opposite sides that are parallel and have no right angles are mainly rhombuses and some irregular parallelograms.