Final answer:
The value of x in angle KNJ of a rhombus quadrilateral JKLM can be found by setting the angle equal to 90 degrees.
Step-by-step explanation:
Since quadrilateral JKLM is a rhombus, the diagonals are perpendicular to each other and bisect each other at point N.
We are given that angle KNJ is equal to 8x + 6.
Since the diagonals of a rhombus are perpendicular, angle KNJ is equal to angle KJM. Therefore, 8x + 6 = 90 degrees.
Solving for x, we subtract 6 from both sides of the equation and then divide by 8: 8x = 84, x = 10.5.
Therefore, the value of x is 10.5.