2 pairs of consecutive congruent sides
yes it can it actually has 2 pairs of consecutife sides that are congruent
parallelogramipio
A kite.
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).
This shape would be a square.
a rhombus
The description given appears to be a 4 sided quadrilateral kite
A square
Angles and sides are congruent when they are identical. A shape with four identical sides and angles is a square.
obtuse
This sounds like a kite, but the wording of the question is not clear. Disjoint and consecutive do not seem to go together.A kite has a pair of congruent sides, which are adjacent, and another pair of congruent sides, which are adjacent.