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The given image shows two parallel lines \( m \parallel n \), and there is a transversal crossing these lines. One of the angles formed by the transversal is \( 146^\circ \), and another angle adjacent to it is marked as \( x^\circ \).

Since the lines \( m \) and \( n \) are parallel, the angles formed by the transversal and the parallel lines follow a specific relationship. The \( 146^\circ \) angle and the \( x^\circ \) angle are **supplementary** angles because they form a linear pair on the same side of the transversal. This means their sum must equal \( 180^\circ \).

Thus, the relationship is:

\[
x + 146^\circ = 180^\circ
\]

Solving for \( x \):

\[
x = 180^\circ - 146^\circ = 34^\circ
\]

Therefore, the value of \( x \) is \( 34^\circ \).

Would you like further details or have any questions?

Here are 5 related questions:
1. What are alternate interior angles, and how do they relate to parallel lines?
2. What is the sum of the angles in a triangle?
3. How can you prove that lines are parallel using angle relationships?
4. What are corresponding angles when two parallel lines are cut by a transversal?
5. What is the relationship between exterior and interior angles in a polygon?

**Tip**: When solving for angles, always check for linear pairs and vertical angles, especially when parallel lines are involved.

Explore how to find the value of x in a problem involving parallel lines and a transversal. Learn about angle relationships, including supplementary and linear pair theorems, and see step-by-step how to solve for the unknown angle.

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