Final answer:
The value of x can be found by setting the expressions for the measures of vertical angles ZA and ZB equal and solving for x. After doing so, we find x = 14; however, this does not match any of the provided options, suggesting there may be an error in the problem or the answer choices.
Step-by-step explanation:
To find the value of x when ZA and ZB are vertical angles, we set the measures of ZA and ZB equal to each other, because vertical angles are equal in measure. That is, m_A = (7x – 27)° and m_B = (3x + 29)° are set to be equal:
7x – 27 = 3x + 29.
Now solve for x:
- Subtract 3x from both sides: 4x – 27 = 29.
- Add 27 to both sides: 4x = 56.
- Divide both sides by 4: x = 14.
However, 14 is not one of the options provided. It seems there might be an error in the problem or the options given. Please double-check the problem or the answer choices. If the question and the options are correctly stated, none of the options match the found value of x.