1. **State the problem:** We have two parallel slanted lines crossed by a horizontal transversal. The angles labeled are $9x^\circ$ (below the transversal, right of the left slanted line) and $3x^\circ$ (above the transversal, right of the right slanted line). We need to find $x$. 2. **Identify the relationship between the angles:** Since the lines are parallel and the transversal crosses them, the angles $9x^\circ$ and $3x^\circ$ are alternate interior angles or corresponding angles depending on their positions. Given the description, these two angles are supplementary because they form a linear pair along the transversal. 3. **Write the equation:** The sum of the angles on a straight line is $180^\circ$, so: $$9x + 3x = 180$$ 4. **Simplify the equation:** $$12x = 180$$ 5. **Solve for $x$:** $$x = \frac{180}{12}$$ 6. **Show cancellation:** $$x = \frac{\cancel{180}}{\cancel{12}} = 15$$ 7. **Final answer:** $$\boxed{15}$$ Thus, $x = 15$ degrees.