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To solve for \( x \) in the given geometric figure, we need to utilize the properties of parallel lines and angles. Here, \( l \parallel m \).

1. Notice that the angles labeled 130° and \( x \) are supplementary because they form a straight line. Therefore:
   \[
   130^\circ + x = 180^\circ
   \]
   Solving for \( x \):
   \[
   x = 180^\circ - 130^\circ = 50^\circ
   \]

2. Now we need to check if there are other relationships. The angle 101° is part of a triangle where the interior angles sum to 180°.

Considering the triangle formed by the 101° angle, the 130° angle, and the top unknown angle:
   \[
   \text{Top angle} + 101^\circ + \text{Other angle} = 180^\circ
   \]
   
From supplementary angles:
   \[
   130^\circ + \text{Top angle} = 180^\circ \implies \text{Top angle} = 50^\circ
   \]

Thus, confirming \( x = 50^\circ \).

Would you like any further details or explanations on this solution?

Here are some additional questions to expand on the topic:

1. What are supplementary angles, and how are they used in geometry?
2. How do the properties of parallel lines affect the angles formed by a transversal?
3. What is the sum of the interior angles of a triangle, and how can it be applied to find unknown angles?
4. How can we determine the types of angles (corresponding, alternate interior, etc.) formed by parallel lines and a transversal?
5. What other geometric principles can be used to solve for unknown angles in more complex figures?

**Tip:** Always check for supplementary and complementary angles when working with parallel lines and transversals. This can simplify finding unknown angles.

Learn how to solve for x in a geometry problem with parallel lines and angles. Understand how to use supplementary angles and the sum of interior angles in triangles to find unknown values. Suitable for students in Grades 8-10.

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