No. An angle can have only one angle!
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Vertical angles
If the parallelogram is a square then angle A is congruent to angle B ,is congruent to angle C. AB is congruent to BC is congruent to CD.
Those are "vertical" angles, even if there's nothing vertical about them.
Angle Angle Side is a method one can use to prove that two triangles are congruent. Basically, if any two pairs of angles and the side between these angles are congruent, then the triangles are congruent as well.
Such angles are called vertically opposite angles.