Question

for what value of x is the given parallelogram a rhombus? the given parallelogram is a rhombus when x =

Explanation:

Step1: Recall property of rhombus

In a rhombus, the diagonals bisect the angles of the rhombus. In a parallelogram that is a rhombus, adjacent - angles are supplementary and also, the angles formed by the diagonals and the sides have a special relationship. Here, we can use the fact that in a rhombus, the adjacent - angles are supplementary. But an easier way is to use the property that the diagonals of a rhombus bisect the angles. So, the two given angles are equal.
Set up the equation: $3x + 34=6x - 2$.

Step2: Solve the equation for x

Subtract $3x$ from both sides of the equation:
$3x+34 - 3x=6x - 2-3x$.
This simplifies to $34 = 3x-2$.
Then add 2 to both sides: $34 + 2=3x-2 + 2$.
We get $36 = 3x$.
Divide both sides by 3: $\frac{36}{3}=\frac{3x}{3}$.
So, $x = 12$.

Answer:

$12$