Final answer:
By setting the alternate angle expressions (6x + 8)° and (7x-2)° equal to each other and solving for x, it is found that the value of x is 10°.
Step-by-step explanation:
The question states that lines x and y are parallel, and that (6x + 8)° and (7x-2)° are alternate angles. In geometry, when two lines are parallel, their alternate angles are equal. Therefore, we set the two expressions equal to each other to find the value of x:
6x + 8 = 7x - 2
To solve for x, we'll subtract 6x from both sides:
8 = x - 2
Then, add 2 to both sides:
x = 10
Therefore, the value of x is 10°.