https://file.aiquickdraw.com/mathbot/file/1726767746479ehd9i8nt.jpg

In the given image, we are asked to find the value of \( x \) in the triangle formed by the angles \( STW \), \( WTV \), and \( STV \).

### Given information:
- \( \angle STV = 135^\circ \)
- \( \angle WTV = 60^\circ \)
- \( \angle STW = x^\circ \) (which is the unknown)

### Steps:
1. Notice that the three angles form a straight line at point \( T \). Thus, the sum of angles around point \( T \) on a straight line is \( 180^\circ \).
   
2. So, we can write:
   \[
   \angle STV + \angle WTV + \angle STW = 180^\circ
   \]
   
3. Substituting the known values:
   \[
   135^\circ + 60^\circ + x^\circ = 180^\circ
   \]

4. Simplifying the equation:
   \[
   195^\circ + x^\circ = 180^\circ
   \]
   \[
   x^\circ = 180^\circ - 195^\circ
   \]
   \[
   x^\circ = -15^\circ
   \]

This result suggests a potential problem, as angle measures cannot be negative in this context. The diagram might need re-interpretation or there could be a conflict with the given setup. Based on a typical geometric diagram, check to ensure all provided information matches correctly.

Would you like more details or to clarify anything? Here are some related questions:

1. Could the arrangement of angles be further clarified or re-checked for other conditions?
2. Could the 135° angle imply an external or reflex measure of a different angle?
3. Could another geometric property, like the total sum of internal angles, help?
4. Do you want a step-by-step check of the exterior angle theorem?
5. Would adding the idea of linear pairs or adjacent angles help resolve this issue?

**Tip:** Always check the provided angle relationships carefully, especially when dealing with lines or parallel setups.

The measure of angle STV is 135°. The measure of angle WTV is 60°. The measure of angle STW is x°. Find the value of x.

Find the value of angle x in a geometry problem involving angle STV = 135° and angle WTV = 60°. Explore the sum of angles on a straight line using basic geometry concepts. Suitable for students in Grades 6-8.

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