https://file.aiquickdraw.com/mathbot/file/1726606205333qzdmowhf.jpg

To solve this problem, we need to use the fact that if two lines, \( m \) and \( n \), are parallel, then the corresponding angles formed by a transversal are equal.

In the image, two angles are given: one is \( 3x^\circ \) and the other is \( (2x + 20)^\circ \). These two angles are alternate interior angles. For the lines \( m \parallel n \), alternate interior angles must be equal.

Therefore, we can set up the equation:

\[
3x = 2x + 20
\]

Now, solve for \( x \):

\[
3x - 2x = 20
\]
\[
x = 20
\]

Thus, the value of \( x \) that makes \( m \parallel n \) is \( x = 20 \).

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

Here are 5 related questions for further exploration:
1. What are corresponding angles, and how do they relate to parallel lines?
2. Can you explain what consecutive interior angles are in parallel lines?
3. How do you find the value of an angle if alternate exterior angles are given?
4. What is the significance of the transversal in geometry involving parallel lines?
5. How can you verify if two lines are parallel using angles?

**Tip:** When solving problems involving parallel lines and angles, always check if the angles are alternate, corresponding, or interior to set up the right equation.

Find the value of x that makes m parallel to n, given the angles 3x and (2x + 20) degrees.

Learn how to find the value of x that makes two lines parallel, using alternate interior angles. This geometry problem involves basic algebra and the Parallel Line Theorem, suitable for students in Grades 8-10.

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