In this diagram, we are given that lines $m \parallel n_1$ and we are asked to find the value of $x$, where angles are formed by a transversal intersecting the parallel lines.

The key observation is that when a transversal cuts through two parallel lines, corresponding and alternate interior angles are equal, and consecutive interior angles are supplementary (they sum to $180^\circ$).

From the diagram:

• There is an angle marked as $120^\circ$ on one side of the transversal.
• $x$ is the angle on the opposite side of the transversal, corresponding to an adjacent interior angle.

Using the consecutive interior angles property: $x + 120^\circ = 180^\circ$

Solving for $x$: $x = 180^\circ - 120^\circ = 60^\circ$

Thus, the value of $x$ is $60^\circ$.

Would you like more details on this or have any additional questions?

Here are some related questions:

1. What is the definition of corresponding angles in parallel lines?
2. Can alternate interior angles be used to solve problems like this one?
3. How do we prove that two lines are parallel using angles?
4. What is the difference between consecutive interior and alternate interior angles?
5. How does the transversal theorem apply to geometry problems?

Tip: When working with parallel lines and a transversal, always look for angle relationships such as corresponding, alternate interior, or consecutive interior angles.