Final answer:
After setting the expressions for alternate interior angles equal to each other and solving for x, the correct value of x is found to be 11.³. However, this does not match any of the answer choices given (20, -8, 7, -6), indicating a possible error in the question or the provided options.
Step-by-step explanation:
When dealing with alternate interior angles, it is important to remember that they are equal when the lines are parallel. The question gives us two expressions for alternate interior angles: (8x - 14)° and (2x + 54)°. To find the value of x, we set these two expressions equal to each other and solve for x.
8x - 14 = 2x + 54
To solve for x, subtract 2x from both sides:
6x - 14 = 54
Now, add 14 to both sides:
6x = 68
Finally, divide both sides by 6 to get:
x = 68 / 6
x = 11.±
However, 11.±3 is not one of the options provided, which suggests there was a calculation error. When repeating the steps correctly, we should find:
x = 68 / 6
x = 11.³
After rechecking the calculations, it is clear that none of the answer choices given (20, -8, 7, -6) match the correct answer of x = 11.³. Therefore, it appears there is a discrepancy between the provided options and the correct calculation.