There are infinitely many such shapes. For example, a hexagon with interior angles measuring 110, 130, 100, 110, 130, 140 degrees. There is one pair of opposite angles each measuring 110 degrees, and a second pair in which each measures 130 degrees.
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A trapezoid.
Such angles are called vertically opposite angles.
A rectangle.
quadrilateral--a four-sided figure, any length sides, any angles trapezoid--one pair of parallel sides, any length sides, any angles parallelogram--two pairs of parallel sides, opposite sides congruent, opposite angles congruent rectangle--two pairs of parallel sides, opposite sides congruent, all angles are right angles (90 degrees) rhombus--two pairs of parallel sides, all sides congruent, opposite angles congruent square--two pairs of parallel sides, all sides congruetn, all angles are right angles (90 degrees)
A parallelogram is a quadrilateral with opposite sides parallel and congruent.