In the given diagram, we see two parallel lines $l$ and $m$, and a transversal intersecting them, forming two angles: one labeled as $104^\circ$ and the other as $(12x - 8)^\circ$.

Since lines $l$ and $m$ are parallel, the angles formed by the transversal will be either corresponding angles or alternate interior angles.

Here, the angle $104^\circ$ and $(12x - 8)^\circ$ are alternate interior angles. For parallel lines, alternate interior angles are congruent (equal). Thus, we can set up the equation:

$12x - 8 = 104$

Solving for $x$:

1. Add 8 to both sides: $12x = 104 + 8$ $12x = 112$

2. Divide both sides by 12: $x = \frac{112}{12}$ $x = 9.33 \ (\text{or } \frac{28}{3})$

Thus, the value of $x$ is approximately $9.33$ or $\frac{28}{3}$.

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Related Questions:

1. What are alternate interior angles in parallel lines?
2. How can we prove that alternate interior angles are equal?
3. What are corresponding angles, and how do they relate to parallel lines?
4. How do you solve for unknowns in angle equations involving parallel lines?
5. Can parallel lines and transversal angles apply to polygons? How?

Tip:

Always look for special angle relationships when you have parallel lines and a transversal. They often simplify solving for unknowns!