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A rhombus would seem to fit the given description
Corgent Angles
Rhombus!
A square. Its opposite sides are equal and it has 4 right angles.
square
This shape has only one pair of opposite sides and no right angles: <
Two opposite right-angles, whose corners share the same crossing point, are vertical angles.
Not necessarily, but it can.
A square or a rectangle perhaps?
One pair of opposite angle is greater than a right angle.
rectangles squares
Yes, and all four sides are equal. The difference is that in the rhombus (tilted square), the angles are not right angles. There are two opposite acute angles and two opposite obtuse angles.