What value of x will make parallelogram ABCD a rhombus?

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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.

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