construct a parallelogram abcd with ab=5.1cm,bc=7cm and angle abc=75

Since, ABCD is a parallelogram, opposite sides are equal. So, AB = CD and BC = AD.

The steps of construction are as follows:

1) Draw a line segment AB = 5.1 cm

2) At B, draw an angle ABX of 75 degrees.

3) With B as centre and 7 cm radius, draw an arc cutting ray BX at C.

4) With C as centre and radius 5.1 cm, draw an arc.

5) With A as centre and radius 7 cm, draw an arc cutting the previous arc at D.

6) Join CD and AD to get the required parallelogram ABCD.