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Yes, the opposite interior angles of a parellelogram are equal.
Generally, there are no right angles in a parallelogram, but rectangles and squares can be seen as special parallelograms, as they have all the qualities needed to be classed as parallelograms, and in addition, they have four right angles.
A parallelogram with equal sides is a rhombus. If the interior angles are right angles, it's a square.
Because they are angles that are subtended by pairs of sides that are parallel to each other. There are several ways of proving the angles are equal.
Yes. A parallelogram is defined as having opposite sides that are parallel and equal in length, and opposite angles that are equal.