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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.
If there are only two parallel lines then 4 corresponding angles will be created
A trapezoid
No angles are formed on the inside of parallel lines because they do not intersect. That is the definition of parallel.
A square "corner" is 90 degrees, (assuming you meant 90 degrees, not 90 angles), and has parallel lines, thus, it must be a parallelogram! A parallelogram that has right angles, is a rectangle. Technically, all that is needed to know is 4 right angles, since all right angles implicate parallel lines and 90 degree angles.