Final answer:
After setting up the equation for vertical angles ZA and B, solving for x yields an answer of 18.33, which does not match any of the given multiple-choice options. There might be an error in the question or options provided.
Step-by-step explanation:
In geometry, when ZA and B are vertical angles, they are equal. Given the equations for ZA and 2B, we can set them equal to each other to find the value of x.
We have ZA = x + 23 and 2B = 5x - 9, but because ZA and B are vertical angles, we know that ZA = B. Therefore, the equations can be written as x + 23 = (5x - 9)/2. Multiplying both sides by 2 to clear the fraction gives us 2x + 46 = 5x - 9.
Solving for x, we subtract 2x from both sides to get 46 = 3x - 9. Adding 9 to both sides gives 55 = 3x, and finally, dividing by 3 gives us x = 18.33, which is not an option in the multiple-choice answers provided.
It seems there may have been a mistake in the formulation of the problem or in the given options, as x does not match any of the answer choices precisely. The closest option to the calculated value of x would be c. x = 18, but it is not exact.