A quadrilateral that fits this description is a trapezoid (or trapezium in some regions) with a specific configuration. In this shape, one pair of opposite sides is parallel, and the angles can be arranged such that two are obtuse and two are acute. For example, one angle might be 120 degrees (obtuse), another 60 degrees (acute), and the remaining angles can be adjusted to maintain the sum of 360 degrees, resulting in two angles that meet the obtuse and acute requirements.
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