The value of x that will make the considered parallelogram ABCD a rhombus is 4 units.
What is rhombus and some of its properties?
Rhombus is a parallelogram whose all sides are of equal lengths.
- Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).
- Its vertex angles are bisected by its diagonals.
- The triangles on either side of the diagonals are isosceles and congruent.
For this problem, the missing figure is attached below.
We see that the angle between the diagonals is [tex](3x- 12)^\circ[/tex]
It is given that ABCD is a parallelogram.
For ABCD parallelogram to be a rhombus, its diagonals need to be perpendicular to each other.
Perpendicular lines have 90° angle between them.
Thus, we need:
[tex](3x- 12)^\circ = 90^\circ[/tex]
Evaluating value of x:
[tex](3x- 12)^\circ = 90^\circ\\3x - 12 = 90\\\text{Adding 12 on both the sides}\\3x = 102\\\text{Dividing both the sides by 3}\\\\x = 12/3 = 4[/tex]
Thus, the value of x is 4
Learn more about rhombus here:
https://brainly.com/question/1542707
