https://file.aiquickdraw.com/mathbot/file/1726239288997b93x6yuh.jpg

In the given figure, the lines \( AB \parallel CD \), and you are tasked with finding the value of \( x \).

Here's how we approach it:

1. The angles \( 130^\circ \) and \( 115^\circ \) are provided as corresponding angles since \( AB \parallel CD \) and \( AC \) acts as a transversal. 

2. According to the diagram, the sum of the three angles at point \( O \) should be \( 180^\circ \) because they form a straight line. These angles are:
   - \( 130^\circ \) (given),
   - \( 115^\circ \) (given),
   - and \( x \) (the unknown).

Thus, the equation can be set up as:
\[
130^\circ + x + 115^\circ = 180^\circ
\]

3. Simplifying the left-hand side:
\[
245^\circ + x = 180^\circ
\]

4. Solving for \( x \):
\[
x = 180^\circ - 245^\circ = -65^\circ
\]

Since a negative angle doesn't make sense in this geometric context, it appears there may be an issue with the figure or provided angles. Could you confirm if the image contains any more relevant information, or there might be a mistake in how the angles are related? 

Feel free to clarify, and I can recheck.

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Do you have any questions or need further clarifications? Here are some related questions that might interest you:

1. How are angles in parallel lines and transversals related?
2. What are corresponding angles, and how can we use them in such problems?
3. How can we determine when angles sum to 180 degrees?
4. Can parallel line problems include negative angles?
5. What is the significance of transversal lines in geometry?

**Tip:** When working with angles and parallel lines, always ensure that the corresponding angles and relationships are clearly understood for accurate results.

In the given figure, AB || CD. Find the value of x.

This problem demonstrates how to find the value of an angle x in a diagram where two parallel lines AB and CD are cut by a transversal AC. Learn the properties of corresponding angles and how to use the sum of angles on a straight line to find unknown angles. Suitable for students in Grades 8-10.

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