Three different quadrilaterals that can have two pairs of opposite angles equal—two acute and two obtuse—are:
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Rectangle: A rectangle has opposite angles that are equal, and each angle is 90 degrees (which can be considered both acute and obtuse in the sense that it can be transformed via different definitions, though typically we do not categorize it as having acute and obtuse angles in standard geometry).
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Cyclic Quadrilateral: A cyclic quadrilateral is one where the vertices lie on a circle. In a cyclic quadrilateral, opposite angles are supplementary. If you construct a cyclic quadrilateral where two of the angles are acute and their opposite angles are obtuse, then it will have two pairs of opposite equal angles.
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Kite: A kite can have two pairs of equal angles; typically, this occurs when the kite is not a rhombus. If we properly design a kite (for example, one where the two adjacent angles are acute, and the other two angles, which are opposite, are obtuse), then it can fit this requirement.
These examples highlight the flexibility of angle measurements in quadrilaterals possessing symmetry in their angles.