No, one of two complementary angles cannot be obtuse, because only two acute angles that add up to 90 degrees are complementary and that an obtuse angle on its own is greater than 90 degrees.
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If you are classifying triangles by their angles, an obtuse triangle has one obtuse angle and two acute angles. A triangle can have at most one obtuse angle. If the two acute angles are congruent, the triangle would also be isosceles.
You know that at least one of them must be acute. A quadrilteral can have three obtuse angles, but not four.
The complementary angles form a right angle with the shared ray.
they could both be right angles
The two angles, other than the right angle itself, MUST be complementary.