Construct a parallelogram ABCD, if :

diagonal AC = 6.4 cm, diagonal BD = 5.6 cm and angle between the diagonals is 75°.

Steps:

1. Draw AC = 6.4 cm.

2. Locate the mid-point O of AC by drawing its perpendicular bisector.

3. Through O, construct a line EOF so that angle EOC = 75°.

4. From OE, cut OB = $\dfrac{BD}{2}$ = $\dfrac{5.6}{2}$ = 2.8 cm and also OD = $\dfrac{BD}{2}$ = $\dfrac{5.6}{2}$ = 2.8 cm

5. Join AB, BC, CD and DA.

Hence, ABCD is the required parallelogram.