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To solve for the angle \( x \), given that lines \( a \) and \( b \) are parallel, we can apply the properties of parallel lines and corresponding or alternate angles. Here's the approach:

### Step 1: Identify relationships between angles
- Since \( a \parallel b \), angles that are on opposite sides of the transversal are alternate interior angles, and corresponding angles are congruent.
  
### Step 2: Analyze the given angles
- The \( 10^\circ \) and \( x \) angles form a triangle with the \( 50^\circ \) angle.
- The sum of angles in a triangle is always \( 180^\circ \).

### Step 3: Set up the equation
In the triangle formed by the angles \( 10^\circ \), \( x \), and \( 50^\circ \):
\[
x + 10^\circ + 50^\circ = 180^\circ
\]

### Step 4: Solve for \( x \)
\[
x + 60^\circ = 180^\circ
\]
\[
x = 180^\circ - 60^\circ = 120^\circ
\]

However, the triangle we are considering is a part of the entire structure. Since we need to use the parallel lines and transversal properties (like corresponding angles), let's break down the geometry further by solving for the specific angles related to this configuration.

Would you like to confirm or proceed with more in-depth explanation on parallel angles? Feel free to ask for clarifications.

Calcular x, si las rectas a y b son paralelas.

Learn how to calculate the angle x by applying the properties of parallel lines and corresponding angles. This problem involves geometry concepts such as the sum of angles in a triangle and alternate interior angles. Suitable for students in Grades 7-9.

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