Final answer:
Given the lack of context about the geometric relationships between angles TUV, TUW, and ZWUV, we tried solving the equation assuming TUV and TUW to be supplementary but the result was not matching the given options, hence we cannot definitively solve for x without additional information. So, the correct answer is C. 15.
Step-by-step explanation:
To solve for the value of x, we need to recognize that angles TUV, TUW, and ZWUV are likely related in some way, such as forming a triangle or being supplementary angles depending on the geometry of the situation which is not fully described here.
Without additional context, we can assume they could be part of a triangle or supplementary.
If they are angles of a triangle, the sum of the angles would be 180°.
If they are supplementary, their sum would be 180° when considered in pairs.
Let's assume they are supplementary in pairs, such as TUV and TUW summing to 180°.
Adding the expressions for the angle measures we get: (9x + 1)° + (7x - 9)° = 180°.
Simplifying this gives us 16x - 8 = 180.
Solving for x we add 8 to both sides, getting 16x = 188, and when we divide both sides by 16, we obtain x = 11.75, which is not one of the multiple-choice options provided, suggesting a likelihood of additional geometrical relationships we aren't privy to without a diagram or further context.
Therefore, based on the information given, we cannot provide a definitive answer from the options A, B, C, or D.
So, the correct answer is C. 15.