https://file.aiquickdraw.com/mathbot/file/1726580028393vi96v769.jpg

We are given three angles: \( \angle TUV = (9x + 1)^\circ \), \( \angle TUW = (7x - 9)^\circ \), and \( \angle WUV = (5x - 11)^\circ \).

From the diagram, it is clear that these three angles form a straight angle at point \( U \), meaning the sum of these angles must equal 180°.

Thus, the equation is:

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

Now, let's solve for \( x \). First, combine like terms:

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

This simplifies to:

\[
21x - 19 = 180
\]

Next, add 19 to both sides:

\[
21x = 199
\]

Finally, divide by 21:

\[
x = \frac{199}{21} \approx 9.48
\]

So, the value of \( x \) is approximately 9.48.

Let me know if you'd like more details or if you have any further questions! Here are five related questions to expand on this:

1. What are the actual measures of \( \angle TUV \), \( \angle TUW \), and \( \angle WUV \) using the value of \( x \)?
2. Can angles form more than a straight line? What would change in such cases?
3. How would the solution change if \( \angle TUW \) had been an exterior angle instead of an interior one?
4. What geometric principles ensure that the sum of angles along a straight line is always 180°?
5. How can we verify if our calculated value of \( x \) is correct by plugging it back into the original expressions?

**Tip**: Always double-check your equation setup to ensure that the sum of angles aligns with known geometric properties (e.g., straight angles or triangles).

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

Find the value of x in the equation where angles m∠TUV = (9x + 1)°, m∠TUW = (7x - 9)°, and m∠WUV = (5x - 11)°. This problem uses algebra and the theorem that the sum of angles on a straight line equals 180°. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation