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To solve this problem, we need to use the information given about the angles formed at point \( U \). The sum of the angles around point \( U \) should be equal to \( 180^\circ \) because they form a straight line.

Given:
- \( m\angle TUV = (9x + 1)^\circ \)
- \( m\angle TUW = (7x - 9)^\circ \)
- \( m\angle WUV = (5x - 11)^\circ \)

The sum of these angles is:

\[
(9x + 1) + (7x - 9) + (5x - 11) = 180
\]

Now, let's solve this equation step-by-step:

1. Combine like terms:

\[
9x + 7x + 5x + 1 - 9 - 11 = 180
\]

\[
21x - 19 = 180
\]

2. Add 19 to both sides:

\[
21x = 199
\]

3. Divide by 21:

\[
x = \frac{199}{21}
\]

Now, let's calculate the value of \( x \).The value of \( x \) is approximately \( 9.48 \).

Would you like further details or have any questions? Here are some related questions for further practice:

1. How do you determine the sum of angles around a point?
2. What steps are involved in combining like terms in an equation?
3. How do you check if your solution for \( x \) is correct in the context of the problem?
4. What are the properties of linear pairs of angles?
5. How can this problem be solved graphically?

**Tip:** Always double-check your calculations, especially when dealing with angles and equations, to avoid simple arithmetic errors!

If m∠TUV = (9x + 1)°, m∠TUW = (7x - 9)°, and m∠WUV = (5x - 11)°, find the value of x.

Learn how to solve for x in a geometry problem where three angles around a point form a straight line. Using algebra and the angle addition postulate, this step-by-step solution is suitable for students in Grades 8-10.

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