The description given could be that of a quadrilateral kite.
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A kite is a quadrilateral with two pairs of adjacent congruent sides. The angles between the unequal sides are equal.
A parallelogram is a geometric quadrilateral with two pairs of parallel sides. The opposite sides and opposite angles are equal in length.
A trapezoid can be drawn to fit the description, as a trapezoid is a quadrilateral with two sides parallel and two sides nonparallel.
It is called a quadrilateral. This is the general term for a four-sided polygon, but if at least two sides are equal or two angles are equal, it has a more specific name.
The base angles of an isosceles triangle that has two equal sides are equal.