1. **State the problem:** We have two parallel lines $m$ and $n$ cut by a transversal. The angles given are $(9x - 13)^\circ$ on line $m$, $(3x - 11)^\circ$ on line $n$, and an adjacent angle $y^\circ$ on line $n$. We need to find $x$ and $y$. 2. **Use the properties of parallel lines and transversals:** Corresponding angles are equal when lines are parallel. So, $$9x - 13 = 3x - 11$$ 3. **Solve for $x$:** $$9x - 13 = 3x - 11$$ $$9x - \cancel{13} + \cancel{13} = 3x - 11 + 13$$ $$9x = 3x + 2$$ $$9x - \cancel{3x} = \cancel{3x} + 2 - \cancel{3x}$$ $$6x = 2$$ $$x = \frac{2}{6} = \frac{1}{3}$$ 4. **Find the value of the angle $(3x - 11)^\circ$:** $$3\times \frac{1}{3} - 11 = 1 - 11 = -10^\circ$$ 5. **Find $y$:** Since $y^\circ$ is adjacent to $(3x - 11)^\circ$ and they form a linear pair, their sum is $180^\circ$: $$y + (3x - 11) = 180$$ $$y + (-10) = 180$$ $$y = 180 + 10 = 190^\circ$$ **Final answers:** $$x = \frac{1}{3}$$ $$y = 190^\circ$$