Angles and sides are congruent when they are identical. A shape with four identical sides and angles is a square.
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).
none exist.
a regular polygon
That is a mathematical impossibility. At least 2 angles have to be congruent in order for the shape to have 4 sides.
square
rectangle
A polygon with 2n sides (n>1) can have opposite angles congruent.
Congruent Figures has equal sides, angles, shape and size.
obtuse
A shape with 4 right angles and 4 equal sides is a square. ==========================
Any rectangle that is not square.