How about a square or a rectangle
a trapeziod
This is a parallelogram. The first requirement is 2 pairs of congruent sides where the congruent sides are not adjacent. This is like a rectangle (excluding a square) that has two pairs of congruent sides where the congruent sides are not adjacent. But the angles are not all congruent (as set in the question) which pushes the shape into the "next less regular" shape, the parallelogram. The angles will not all be congruent, but it will have 2 pairs of congruent angles. There is no way to avoid the 2 pairs of congruent angles because of the requirement that the shape must have 2 pairs of congruent sides (the first requirement).
A polygon with 2n sides (n>1) can have opposite angles congruent.
Angles and sides are congruent when they are identical. A shape with four identical sides and angles is a square.
It could be a hexagon which is stretched out so that one pair of opposite angles become acute - but they must be different otherwise you will have three pairs of parallel sides.
its a shape
It could be a hexagon which is stretched out so that one pair of opposite angles become acute - but they must be different otherwise you will have three pairs of parallel sides.
rectangle
No. A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel. The opposite angles not congruent.
obtuse
A Rectangle
an isosceles triangle