This is a geometry problem involving parallel lines and transversals. Let's solve for $x$ step by step.

Observations:

1. The lines $l$, $m$, and $n$ are parallel ($l \parallel m \parallel n$).
2. A transversal intersects these lines, forming several angles.
3. The given angles are:
   • $30^\circ$ (an interior angle near $x$).
   • $130^\circ$ (an exterior angle on the lower parallel line $n$).

Steps to Solve:

1. Find the corresponding interior angle to $130^\circ$:

   • $130^\circ$ and its adjacent angle on the same line form a linear pair.
   • The adjacent angle is: $180^\circ - 130^\circ = 50^\circ$
   • This $50^\circ$ corresponds to the angle directly above it on line $m$ because of the parallel lines and the transversal.

2. Use the angle sum property near $x$:

   • At the intersection near $x$, the angles $x$, $30^\circ$, and $50^\circ$ are angles around a point. The sum of these angles is: $x + 30^\circ + 50^\circ = 180^\circ$

3. Solve for $x$: $x = 180^\circ - 30^\circ - 50^\circ$ $x = 100^\circ$

Final Answer:

$x = 100^\circ$

Would you like a more detailed breakdown of any specific step? Let me know!

Related Questions:

1. What are corresponding angles in parallel lines and transversals?
2. How does the linear pair property help solve such problems?
3. What are the other angles at the intersection points in this diagram?
4. Can alternate interior angles be used to verify the result?
5. How do parallel lines simplify angle calculations?

Tip:

Always identify pairs of corresponding, alternate, or supplementary angles when dealing with parallel lines and transversals to simplify your solution!