This image represents two intersecting lines, forming two angles. The two angles appear to be corresponding angles, which means they are equal. To find $x$, we can set the expressions for the two angles equal to each other.

The angles given are: $(15x + 4)^\circ \quad \text{and} \quad (12x + 16)^\circ$

Since these are corresponding angles, we can set the expressions equal to each other: $15x + 4 = 12x + 16$

Solving for $x$:

1. Subtract $12x$ from both sides: $15x - 12x + 4 = 16$ $3x + 4 = 16$

2. Subtract 4 from both sides: $3x = 12$

3. Divide both sides by 3: $x = 4$

Thus, $x = 4$.

Would you like further details or have any questions about this solution?

Related questions:

1. What are the properties of corresponding angles in geometry?
2. How do we verify if two lines are parallel using angles?
3. What are alternate interior angles, and how do they differ from corresponding angles?
4. Can two angles be supplementary in a similar setup? How can you check that?
5. How would this problem change if the lines were not parallel?

Tip: Always double-check the type of angles involved (corresponding, alternate, etc.) when solving geometry problems involving parallel lines.