How does one determine the angles formed by the inersection of the two diagonals of a parallelogram?

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.