congruent
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congruent complements
None! If the angles are not congruent then the shapes are not similar of congruent. But that is not a problem. The angles of an equilateral triangle are not congruent to the angles of a square but that does not mean that you cannot work with equilateral triangles or squares!
Two angles are said to be congruent if they are equal.
No. Angles are not congruent. (Triangles may be congruent.)
No, complementary angles aren't normally congruent.