Parallel lines do not meet and so cannot form an angle.
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When a transversal line cuts through parallel lines various angles are created such as equal corresponding angles and equal alternate angles as well as other types of angles.
If there are only two parallel lines then 4 corresponding angles will be created
If the two lines are parallel, then you get 4 pairs of vertical angles. If the two lines are not parallel, then we get 6 pairs of vertical angles.
The angles between the sides that are parallel are congruent.The angles between the sides that are parallel are congruent.The angles between the sides that are parallel are congruent.The angles between the sides that are parallel are congruent.
In two dimensions, lines can be parallel, angles cannot. So no plane shape has parallel angles.