Q: What has 4 equal sides and 2 pairs of equal angles that are not congruent?

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Yes, a rhombus always has two pairs of congruent angles because of the fact that all of their sides are equal.

A rhombus would fit the given description because it has 4 equal sides with 2 equal acute angles and 2 equal obtuse angles.

No but it has congruent base angles. Also it has: One pair of parallel sides Non-parallel sides that are equal Two pairs of equal angles Diagonals that are equal

A General Quadrilateral

Two pairs of congruent angles and one pair of congruent sides ( sides not between the pairs of angles ).

Related questions

a square 2 pairs of equal angles: A rhomboid

Yes, a rhombus always has two pairs of congruent angles because of the fact that all of their sides are equal.

A parallelogram

A rhombus would fit the given description because it has 4 equal sides with 2 equal acute angles and 2 equal obtuse angles.

A kite is a quadrilateral with two pairs of adjacent congruent sides. The angles between the unequal sides are equal.

No but it has congruent base angles. Also it has: One pair of parallel sides Non-parallel sides that are equal Two pairs of equal angles Diagonals that are equal

A rhombus is a parallelogram with four equal sides. A square is a type of rhombus.

This is a rectangle.

A rectangle

A rectangle (that is not a square).

A General Quadrilateral

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).