A parallelogram is a convex quadrilateral with two sets of parallel sides. The parallel sides are opposite to one another.
The diagonals of a parallelogram bisect each other. Therefore, the point of intersection is located exactly half way along each diagonal.
Opposite angles in a parallelogram are congruent (equal).
Consecutive (adjacent) angles in a parallelogram are supplementary (totaling 180 degrees)
As to the angles formed by the intersection of the diagonals of a parallelogram, adjacent angles are supplementary (totaling 180 degrees). The opposite angles are congruent (equal).
Using these relationships, plus knowledge that the 3 internal angles of a triangle total 180 degrees, it is possible to calculate the various angles in a parallelogram if the value of one of the angles is given.
Please see the reference for an excellent graphic representation and explanation of these rules as they apply to a parallelogram.