No. An obtuse angle is an angle whose measure is greater than 90 degrees. If there are two angles whose measures are greater than 90 degrees, then there is no possible way that the sum of the two could be equal to 90 degrees and thus be characterized as complimentary angles.
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No not ever because the 3 interior angles of any triangle add up to 180 degrees and so an obtuse triangle will have 1 obtuse and 2 acute angles.
Yes, a quadrilateral can have 2 obtuse angles.
No but they can have 2 obtuse and 2 acute angles
A rhombus has 2 obtuse angles
An obtuse triangle has 1 obtuse angle and 2 acute angles