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The problem provided involves parallel lines and corresponding angles.

In the figure:
- Two lines, \( l \) and \( m \), are parallel.
- The angle given is \( 75^\circ \).
- The corresponding angle is \( x \), as shown in the diagram.

Since \( l \parallel m \), the angles formed on a transversal are either corresponding angles, alternate interior angles, or supplementary angles. Here, \( x \) is a corresponding angle to the given \( 75^\circ \) angle.

**Corresponding angles** are equal when two lines are parallel. Therefore, \( x = 75^\circ \).

So the correct answer is:

**Option (a) \( x = 75^\circ \)**.

Would you like further clarification or details on how parallel lines and angles work? Here are five related questions for practice:

1. What are alternate interior angles?
2. How do we prove that two lines are parallel using angles?
3. What is the relationship between consecutive interior angles on a transversal?
4. Can supplementary angles exist between parallel lines? If yes, how?
5. What are vertical angles, and how are they related to parallel lines?

**Tip:** Remember that corresponding angles on parallel lines are always equal.

In the adjoining figure, if l || m, then the value of x is

Learn how to find the value of x in a geometric figure where two parallel lines are cut by a transversal. This question uses the corresponding angles theorem to show that x = 75°. Suitable for students in Grades 8-10.

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