Two types of quadrilaterals that can have two acute angles and two obtuse angles are:
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Trapezoid (or Trapezium): In certain configurations, a trapezoid can have two acute angles and two obtuse angles, especially if the non-parallel sides are angled in such a way.
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Kite: A kite can also exhibit this angle configuration if it has one pair of opposite angles that are acute and the other pair that is obtuse.
Both of these quadrilaterals can have the specified angle types depending on their specific dimensions and angles.