Construct a rectangle ABCD; if :

each diagonal is 5.5 cm and the angle between them is 60°.

Steps:

1. Draw AC = 5.5 cm.

2. Draw the perpendicular bisector of AC to locate the mid-point of AC. Let the perpendicular bisector intersect AC at point O. Therefore, O is the mid-point of AC.

3. Through O, construct a line EOF so that angle EOC = 60°.

4. From OE cut OB equal to OC (i.e., 2.7 cm) and from OF cut OD equal to OA (i.e., 2.7 cm).

5. Join AB, BC, CD and DA.

Hence, ABCD is the required rectangle.