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A 'KITE' ; two adjacent sides may be of equal length. A parallelogram has two pairs of equal and parallel sides.
Any shape with more than 3 sides can have two pairs of equal sides and no right angles. If it only has 4 sides in total and isn't a parallelogram, then it's a trapezoid.
Not always. A parallelogram only has to have two equal parallel sides and its angles does not have to be 90°. Only two types of parallelogram, the rectangle and the square, have four right angles.
All squares have TWO SETS of opposite, parallel sides. A square is a parallelogram with 4 equal sides and 4 equal angles (right angles) of which adjacent sides are perpendicular. The related parallelogram, the rhombus, or "diamond" shape, also has 4 equal sides, but no right angles, where opposite angles are equal and adjacent angles are supplementary (sum to 180 degrees).
A parallelogram would fit the given description because it has a two parallel sides with 2 equal acute angles and 2 equal obtuse angles.