It is not possible for a quadrilateral in Euclidean plane geometry to have no equal angles and still have its opposite sides parallel.It's possible for a quadrilateral to have no equal angles and two of its sides parallel (opposite ones, obviously; adjacent sides can't possibly be parallel). That would be a trapezoid.
Yes, the opposite angles in a regular quadrilateral are equal.
rhombus. The rhombus is a quadrilateral with all sides equal in length. It is also a parallelogram, so opposite sides are parallel and equal in length, and opposite angles are equal.
A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal
All quadrilaterals apart from rectangles. Even parallelograms have adjacent angles that are not equal.
a rhombus, a quadrilateral without right angle, a quadrilateral with equal opposite parallel sides but no right angles
A rhombus is a 4 equal sided quadrilateral with opposite parallel sides and equal opposite acute angles and equal opposite obtuse angles that all add up to 360 degrees.