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It is a trapezoid that can have two right angles plus one obtuse angle plus one acute angle and the four angles add up to 360 degrees.

Q: What quadrilateral has two right angles only one set of parallel sides and no lines of symmetry?

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It is called a Rhombus.

A quadrilateral with 4 right angles can only be a rectangle or a square. A rectangle has only two lines of symmetry - the lines joining the midpoints of its opposite sides. So the answer cannot be a rectangle. A square has the same lines of symmetry as a rectangle, plus the two diagonals - 4 lines in all.

I don't think this is possible. there is not a quadrilateral with these qualities. If it is a quadrilateral, it will automatically have parallel lines, but there is not one that has both. The closest one would be the trapezoid, with a set of parallel lines, but no right angle. The square and rectangle have two sets of parallel lines and 4 right angles.

A right angle trapezoid

Related questions

This is a parallelogram.

A Rhombus.

Parrallelogram (it has rotational symmetry but no lines of symmetry)

A trapezoid is a quadrilateral with a set of parallel lines. Because it is a quadrilateral, it has four angles.

square

A trapezoid.

Parallelogram

rectangle

A square has.

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trapezoid

Such a shape cannot exist.