In geometry two figures are congruent if they have the same shape and size if they are non congruent they do not have the same shape and size
two triangles are congruent if their corresponding sides are all equal in lengh and their corresponding angles are equal in size
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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!
A congruent angle can also mean equal angle. So there is no set measurement of a congruent angle. Just the same as the angle it is equal to.
If by "equal" you mean "equal in length", yes, that is the same as "congruent".
It means congruent
The angles formed by one congruent side adjacent to the side not congrent to the first side