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In this diagram, two parallel lines (JK and LM) are intersected by a transversal (HI). The angles \((3x + 25)^\circ\) and \((4x - 10)^\circ\) are formed at the points of intersection. Since JK and LM are parallel, we can apply the rule that corresponding angles are equal.

The angle \((3x + 25)^\circ\) is corresponding to the angle \((4x - 10)^\circ\), so:

\[
3x + 25 = 4x - 10
\]

Now, let's solve for \(x\):

1. Subtract \(3x\) from both sides:
\[
25 = x - 10
\]

2. Add 10 to both sides:
\[
35 = x
\]

Thus, \(x = 35\).

Would you like more details or have any further questions?

### Related Questions:
1. What are alternate interior angles, and how can they be used in similar problems?
2. How can the concept of supplementary angles be applied when working with transversals?
3. Are there any other ways to verify if two angles are congruent in parallel line setups?
4. What happens if the lines are not parallel but you still use transversal properties?
5. How does solving for angles in geometry differ when working with polygons?

**Tip:** When solving for unknowns using angles in parallel lines, always check if the angles are corresponding, alternate interior, or supplementary to determine equality.

Solve for x. In the given diagram, two parallel lines (JK and LM) are intersected by a transversal (HI). The angles (3x + 25)° and (4x - 10)° are formed at the points of intersection.

Learn how to solve for x in a geometry problem involving parallel lines and a transversal. The angles (3x + 25)° and (4x - 10)° are given. Using the corresponding angles postulate, find the value of x with a detailed step-by-step solution. Suitable for students in Grades 8-10.

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