https://file.aiquickdraw.com/mathbot/file/1726967221054y83mzwt2.jpg

Let's focus on solving the problem in the image, particularly question 23, which asks for the value of \( x \), with the given diagram.

### Step-by-step analysis:

1. **Identify angles from the diagram**:
   - We are given two angles at the bottom part of the shape: one is \( 65^\circ \), and the other is \( y \).
   - Another angle at the top of the diagram is \( 50^\circ \), adjacent to \( x \).

2. **Relationship between angles**:
   - Based on the arrows on the sides of the diagram, it appears that the figure includes two sets of parallel lines. We can use the fact that interior angles on the same side of a transversal add up to \( 180^\circ \) (supplementary angles).
   
   - The angle at the bottom left \( 65^\circ \) and angle \( y \) are on the same side of a transversal (parallel lines), so:
     \[
     65^\circ + y = 180^\circ
     \]
     Solving for \( y \):
     \[
     y = 180^\circ - 65^\circ = 115^\circ
     \]

3. **Finding \( x \)**:
   - Now we move to the top part of the figure. Angle \( 50^\circ \) and angle \( x \) are also on the same side of the transversal (parallel lines), so:
     \[
     50^\circ + x = 180^\circ
     \]
     Solving for \( x \):
     \[
     x = 180^\circ - 50^\circ = 130^\circ
     \]

### Final Answer:
The value of \( x \) is **130°**.

Would you like further details or have any questions?

Here are 5 related questions you can explore:
1. How do you find the value of supplementary angles?
2. What are alternate interior angles and how are they used in parallel line problems?
3. What is the sum of the interior angles of a polygon?
4. How do parallel lines and transversals affect angle relationships?
5. Can vertical angles ever be supplementary?

**Tip**: When working with parallel lines and transversals, always look for corresponding or alternate interior angles to simplify the problem!

What is the value of x, given that the angles include 50° and 65° in a parallelogram-like figure with parallel lines?

Solve the geometry problem involving supplementary angles and parallel lines to find the value of x. Given angles include 50° and 65°, and the solution uses key geometric concepts and theorems about transversals. Suitable for students in Grades 7-9.

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