The problem suggests that two lines $m$ and $n$ are parallel, denoted by $m \parallel n$, and angles are provided on a transversal $t$ that cuts through these parallel lines.

From the diagram, I assume:

• $(6x + 4)^\circ$ represents one of the angles formed by the intersection of the transversal $t$ with line $m$,
• $(2x + 16)^\circ$ represents another angle formed by the intersection of the transversal $t$ with line $n$.

Since $m \parallel n$, we can use the properties of angles formed by a transversal cutting through parallel lines. Specifically:

• Corresponding angles are equal.
• Alternate interior angles are equal.
• Alternate exterior angles are equal.

Steps to find $x$:

If $(6x + 4)^\circ$ and $(2x + 16)^\circ$ are corresponding angles (or any other angles that should be equal), we can set up the equation:

$6x + 4 = 2x + 16$

Now, solving for $x$:

1. Subtract $2x$ from both sides:

$6x - 2x + 4 = 16$

2. Simplify:

$4x + 4 = 16$

3. Subtract 4 from both sides:

$4x = 12$

4. Divide by 4:

$x = 3$

Thus, the value of $x$ is $\boxed{3}$.

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Do you want details or have any questions?

Here are some related questions for further exploration:

1. What are corresponding angles and how do they relate to parallel lines?
2. How would you solve if the angles were alternate interior angles instead of corresponding angles?
3. What other angle relationships occur when a transversal cuts through parallel lines?
4. If the angle expressions were different, how would you set up a new equation?
5. How can you check if the value of $x$ satisfies the angle properties of parallel lines?

Tip: When solving for variables in geometry, always check the relationships between angles—like corresponding, alternate interior, or same-side interior angles.