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. So, the adjacent - angles of the given parallelogram (which will be equal in a rhombus) are equal. Set the two given angle - expressions equal to each other: $2x + 34=8x - 2$.

Step2: Solve the equation for x

First, subtract $2x$ from both sides:
$2x+34 - 2x=8x - 2-2x$
$34 = 6x-2$.
Then, add 2 to both sides:
$34 + 2=6x-2 + 2$
$36 = 6x$.
Finally, divide both sides by 6:
$\frac{36}{6}=\frac{6x}{6}$
$x = 6$.

Answer:

$6$