The image contains a problem that asks to find the value of $x$ for which lines $m \parallel n$. Two angles are given:

• $(4x - 28)^\circ$
• $(3x + 11)^\circ$

Since the lines $m \parallel n$, these angles are corresponding angles and must be equal because corresponding angles are congruent when two lines are parallel. Therefore, we can set up the equation:

$4x - 28 = 3x + 11$

Solving the equation:

1. Subtract $3x$ from both sides: $4x - 3x - 28 = 11$ $x - 28 = 11$

2. Add 28 to both sides: $x = 11 + 28$ $x = 39$

Thus, the value of $x$ is 39.

Would you like further details, or do you have any other questions about this?

Here are 5 related questions to explore this concept further:

1. What are alternate interior angles and how do they relate to parallel lines?
2. How can you verify if two lines are parallel using angles?
3. What happens if the angles given were not equal—could the lines still be parallel?
4. Can you solve for the angles when $x = 39$?
5. What are other methods to prove lines are parallel?

Tip: Always check whether the angles you're working with are corresponding, alternate interior, or exterior, as this helps in setting up the correct equation.