Answer: The value of x=34 will make parallelogram ABCD a rhombus.
Step-by-step explanation:
Given a parallelogram ABCD where AC and BD are diagonal intersecting at E such that ∠AEB=(3x-12)°........(1)
To make it rhombus ∠AEB should be 90° (∵ diagonals of rhombus are perpendicular bisector of each other)
Substitute ∠AEB =90° in (1) we get
(3x-12)°=90°
⇒3x-12=90
⇒3x=90+12[adding 12 on both sides]
⇒3x=102
Dividing 3 from both sides, we get
⇒x=34
Therefore ,the value of x =34 will make parallelogram ABCD a rhombus.
