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

Expert Answers
boblawrence eNotes educator| Certified Educator

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.