square or rectangle
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This shape has only one pair of opposite sides and no right angles: <
A cyclic kite. A kite is cyclic if it has only two right angles.
A shape with five sides would be a pentagon, but a shape can not have 5 right angles. Squares and Rectangles are both shapes with 4 sides and 4 right angles. They are the only shape with the same amount of right angles as there is sides.
Yes, a trapezoid can have two right angles and two acute angles. Its only requirement is that it has two parallel sides.
A rectangle is the only such shape. Not sure about the "little" right angles: all right angles are of the same measure.