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Angles are usually illustrated as two acute and two obtuse, but there can be two right, one acute and one obtuse. Angles cannot be parallel since that is a characteristic of lines, not angles!
No, a trapezoid does not have four obtuse angles. A trapezoid has one pair of parallel sides and the other pair of non-parallel sides. The angles of a trapezoid can be a combination of acute, obtuse, and right angles, but it cannot have four obtuse angles.
A parallelogram is a quadrilateral with opposite sides parallel and congruent.
trapezoid
If two of the angles of a parallelogram are acute, then the other two angles will be obtuse. Since a parallelogram contains two pairs of parallel sides, both of the acute angles and both of the obtuse angles respectively will measure the same.