Can two Adjacent Angles be Supplementary

Is it possible to add two adjacent angles? As the only demands on the two angles are: your readings sum up to 180 (or $\pi$ radians),... two arbitrary intersection rules (or a beam formed on one rule) make at least one adjacent additional set of angles.

Here the FI and HJ line cross at point E1; one of the angles shown in figure 1 and one of the angles shown in figure 2 make adjacent additional angles.

Here line AB and beam CD cross at C; the generated angles of amber and violet are an adjacent, additional couple. "Supplementary " refers to the relation of the dimension of two angles. "Adjacent " refers to the geometrical relation between the angles. Additional angles have a dimension that amounts to 180. Think of two different angles, e.g. 45 and 80 degree.

They are not complementary. Just think, one of the angles is on the moon and the other on Jupiter. Clearly, they're not side by side. Neighboring angles should make a straight line couple. Is it possible to add two adjacent angles? Of course, these two angles are both side by side and complementary:

Additional angles are two angles that sum up to 180 degree. You' ve now plotted two angles, both with the same apex. These two angles sum up to 180-degree. These two angles are adjacent angles. These two angles are complementary angles. This gives you two adjacent angles that are complementary.

COULD TWO ADJACTIVE ANGLES be COMPLETE???????????????????? Line and angle mathematics?