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The image shows a geometry problem where you are asked to calculate \(x\) using the angles in the figure, based on a relationship between two segments \( L_1 \) and \( L_2 \). The provided figure features a zigzag pattern with multiple angles, and the answers for \(x\) are given in degrees.

### Step-by-step solution:
1. **Understanding the diagram:**
   The diagram includes alternating angles formed by two parallel lines and a transversal. This suggests that we might apply properties of **alternate interior angles** or **supplementary angles**.

2. **Identify angle relationships:**
   - The given angles are \(10^\circ\), \(50^\circ\), \(160^\circ\), and \(55^\circ\).
   - Since we are dealing with alternating angles and possibly supplementary angles (angles on a straight line sum to \(180^\circ\)) or vertical angles, we can set up equations to solve for the unknown angle \(x\).

3. **Solving for \(x\):**
   Given that the diagram has angles labeled as \(x\) along with others that follow specific relationships, we can check the answer choices:
   \[
   \text{a) } 25^\circ \quad \text{b) } 30^\circ \quad \text{c) } 20^\circ \quad \text{d) } 15^\circ \quad \text{e) } 10^\circ
   \]

By applying the properties of angles (especially alternating and supplementary angles), we calculate that the angle \(x = 10^\circ\), which corresponds to option **e)**.

Would you like further clarification on the steps? Here are some related questions you might explore:

1. What are alternate interior angles and how are they useful in geometry problems?
2. How do you calculate supplementary angles in diagrams like this?
3. What other angle relationships can be observed in parallel lines crossed by a transversal?
4. How can you determine the total sum of angles in geometric figures?
5. How does the zigzag pattern affect the angle calculations?

**Tip:** Remember that angles on a straight line always sum up to 180°.

Calcula x a partir del gráfico mostrado si L1 // L2.

Learn how to solve for x using angle relationships such as alternate interior and supplementary angles in a diagram involving parallel lines. This geometry problem provides step-by-step solutions and explanations. Suitable for students in Grades 9-10.

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