Question: Given $m \parallel n$, find the value of $x$.
$(6x-8)^\circ$
$(2x+4)^\circ$
Answer
$x = $
1. **State the problem:** We are given two parallel lines $m$ and $n$ cut by a transversal $t$. We need to find the value of $x$ given the angles $(6x-8)^\circ$ and $(2x+4)^\circ$.
2. **Identify the relationship between the angles:** Since $m \parallel n$ and $t$ is a transversal, the angles given are alternate interior angles.
3. **Property used:** Alternate interior angles are equal when lines are parallel.
4. **Set up the equation:**
$$6x - 8 = 2x + 4$$
5. **Solve for $x$:**
$$6x - 8 = 2x + 4$$
$$6x - \cancel{8} + \cancel{8} = 2x + 4 + 8$$
$$6x = 2x + 12$$
$$6x - 2x = 12$$
$$4x = 12$$
$$x = \frac{12}{4}$$
$$x = 3$$
6. **Final answer:**
$$\boxed{3}$$