https://file.aiquickdraw.com/mathbot/file/1727285374454a2azdnro.jpg

The image shows a set of intersecting lines, forming vertical angles, along with two algebraic expressions representing the measures of certain angles.

Here’s how to solve for angle 1:

1. **Identify relationships**: The angles labeled as \(8x - 4\) and \(6x + 8\) are *alternate interior angles* because they are on opposite sides of the transversal and between the parallel lines. This means they are equal in measure.

2. **Set the angles equal**: 
   \[
   8x - 4 = 6x + 8
   \]

3. **Solve for \(x\)**:
   \[
   8x - 6x = 8 + 4
   \]
   \[
   2x = 12
   \]
   \[
   x = 6
   \]

4. **Substitute \(x = 6\) into one of the expressions** to find the measure of angle 1. Let's use \(6x + 8\):
   \[
   6(6) + 8 = 36 + 8 = 44^\circ
   \]

So, **angle 1 measures \(44^\circ\)**.

Would you like further details or have any questions?

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Here are five related questions:
1. How can you verify if two lines are parallel using alternate interior angles?
2. What are corresponding angles, and how do they relate to parallel lines?
3. Can you explain vertical angles and how they behave when lines intersect?
4. How do you set up equations when dealing with consecutive interior angles?
5. What is the definition of a transversal in geometry?

**Tip**: Always look for angle relationships like alternate interior, vertical, or corresponding angles when dealing with parallel lines. These can help set up equations to find unknown values.

Learn how to solve for the measure of angle 1 using the alternate interior angle theorem. This problem involves solving linear equations and understanding angle relationships in parallel lines. Suitable for students in Grades 7-9.

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