https://file.aiquickdraw.com/mathbot/file/1730295088671i9aod66v.jpg

To find the value of \( x \) that makes line \( a \parallel b \), we need to analyze the angle relationships in the diagram. Here’s the solution process:

### Step-by-Step Solution

1. **Identify Corresponding Angles:**
   When two lines are parallel and cut by a transversal, corresponding angles are equal. 
   Here, angle \( \angle 2 \) and angle \( \angle 7 \) are corresponding angles. 

2. **Set Up the Equation Using Corresponding Angles:**
   Given:
   \[
   m \angle 2 = (3x + 15)^\circ
   \]
   \[
   m \angle 7 = 105^\circ
   \]
   Since \( a \parallel b \), \( \angle 2 = \angle 7 \). So we set up the equation:
   \[
   3x + 15 = 105
   \]

3. **Solve for \( x \):**
   - Subtract 15 from both sides:
     \[
     3x = 90
     \]
   - Divide by 3:
     \[
     x = 30
     \]

### Conclusion
The value of \( x \) that makes \( a \parallel b \) is \( \mathbf{30} \).

Would you like more details on any step, or do you have additional questions?

### Related Questions
1. What are corresponding angles, and how are they identified?
2. How does the transversal line affect the angles in this problem?
3. What are other types of angle relationships that occur when two lines are parallel?
4. Can alternate interior angles help in proving lines parallel?
5. How would the solution change if the angle measurements given were different?

#### Tip
In problems involving parallel lines, always look for relationships like corresponding, alternate interior, or alternate exterior angles to set up equations easily.

Given m∠2 = (3x + 15)° and m∠7 = 105°, find the value of x that makes a // b.

Explore how to find the value of x to make lines parallel by applying the Corresponding Angles Postulate. Given m∠2 = (3x + 15)° and m∠7 = 105°, we set up and solve an equation to determine x. Perfect for students in Grades 8-10.

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