angles between diagonals parallelogram

     d blue1    - smaller  diagonal

     DD blue    - larger  diagonal

    a black , b black     -  sides of a parallelogram

     alpha red  -  acute angle  between diagonals

     beta green  - obtuse angle  between diagonals

   A18 black    -  area of a parallelogram

 

Formulas for calculating angles between diagonals if given sides and diagonals  :

angles between diagonals parallelogram F1

angles between diagonals parallelogram F2

 

angles between diagonals parallelogram F3

angles between diagonals parallelogram F4

 

Formula for calculating angle between diagonals if given area of a parallelogram and diagonals  :

angles between diagonals parallelogram F5

 

Formulas for the relation of the acute and obtuse angles between diagonals:  :

angles between diagonals parallelogram F6