https://file.aiquickdraw.com/mathbot/file/17262620102569z6lcbw2.jpg

Let's analyze the diagram to determine the measure of angle 1:

### Key observations:
- Two parallel lines are given (denoted as line \(a\) and line \(c\)), and a transversal intersects them, forming angles at two points.
- Angle measures are given as \(2x^\circ\) and \((4x - 60)^\circ\), and we need to find the value of angle 1.

Since the lines are parallel and the transversal forms angles, we can apply properties of parallel lines and transversals, specifically **alternate interior angles** and **corresponding angles**.

### Step-by-step solution:

1. **Identify the relationship between the angles:**
   - \(2x^\circ\) is one of the angles on the top left, and \((4x - 60)^\circ\) is on the bottom right, both being alternate interior angles because they lie on opposite sides of the transversal and between two parallel lines.

2. **Set up the equation:**
   According to the alternate interior angle theorem:
   \[
   2x = 4x - 60
   \]

3. **Solve for \(x\):**
   \[
   2x = 4x - 60
   \]
   \[
   60 = 4x - 2x
   \]
   \[
   60 = 2x
   \]
   \[
   x = 30^\circ
   \]

4. **Substitute \(x = 30^\circ\) into \(2x^\circ\):**
   \[
   2x = 2(30) = 60^\circ
   \]
   So, angle 1 measures \(60^\circ\).

### Conclusion:
The correct answer is **A**: The measure of angle 1 is \(60^\circ\).

Would you like any further details or clarification?

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Here are 5 related questions for further exploration:
1. What are alternate interior angles and why are they congruent when lines are parallel?
2. How would the answer change if the lines were not parallel?
3. What is the difference between alternate interior and corresponding angles?
4. Can angle 1 still be calculated if one of the equations were missing?
5. How can the angle sum property of triangles help in determining angle measures in such diagrams?

**Tip:** When working with parallel lines and a transversal, always check for angle relationships like alternate interior, corresponding, and supplementary angles!

In the diagram, two measures of angles are given in algebraic form. Which statement is true about angle 1?

Discover how to determine the measure of angle 1 using algebraic equations and the Alternate Interior Angle Theorem in a geometry problem involving parallel lines and transversals. A step-by-step solution for Grade 8 students.

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