An angle greater than 90 degrees in measure.
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The definition of an obtuse angle is that it is greater than 90 degrees and less than 180. By this definition, the smallest obtuse angle you can have is 90.00001 degrees, with infinite 0's.
a triangle that contains an obtuse interior angle
An obtuse angle is an angle that is larger that 90 degrees but smaller than a straight angle (180 degrees).
Because an obtuse angle is greater than 90 degrees by definition and a right angle is 90 degrees by definition, so an obtuse triangle would need to have both a right angle and an obtuse angle, which would exceed the number of degrees than a triangle can have, which is 180 degrees.
Two angles are complementary when they add up to exactly 90 degrees. An obtuse angle is by definition greater than 90 degrees. Therefore, an obtuse angle cannot have a complementary angle. So an obtuse angle and an acute angle are never complementary.