Parallel lines do not meet. Therefore they do not form any angles! So the angles (that do not exist) cannot add up to anything.
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No, two lines would not be parallel if the consecutive interior angles measured 108 degrees and 74 degrees. Consecutive interior angles on parallel lines are always congruent, meaning they have the same measure. Therefore, if the consecutive interior angles have different measures, the lines cannot be parallel.
Triangles do not have parallel lines but as right angles triangles they do have perpendicular lines that meet at 90 degrees.
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.
No, right angles are the same as perpendicular. A right angle means that 2 lines intersect at 90 degrees which makes them perpendicular. Two lines that are parallel do not intersect at all.
If the two lines are parallel, they will never connect. A straight line drawn across those lines will intersect them at identical angles. If you have perpendicular lines, they intersect and all four angles that they make are 90 degrees.