In this image, you are asked to find the value of $x$ that makes lines $A \parallel B$. When two lines are parallel, corresponding angles are equal.

Key Information:

• Angle 1 on line $A$: $3x$
• Angle 2 on line $B$: $6x + 45$

For $A \parallel B$, these two corresponding angles must be equal:

$3x = 6x + 45$

Solving the equation:

1. Subtract $6x$ from both sides: $3x - 6x = 45$ $-3x = 45$

2. Divide both sides by $-3$: $x = -15$

Thus, $x = -15$.

Would you like more details or have any further questions?

Related Questions:

1. What are corresponding angles, and how do they relate to parallel lines?
2. Can parallel lines ever meet if extended infinitely?
3. What are alternate interior angles, and how do they relate to parallel lines?
4. How do the slopes of parallel lines compare in Cartesian geometry?
5. What other geometric properties can help determine whether two lines are parallel?

Tip:

Always remember that for two lines to be parallel, corresponding angles formed by a transversal must be equal.