1. **State the problem:** We need to find values of $x$ and $y$ such that lines $l$ and $m$ are parallel. Given angles are $(17x + 14)^\circ$, $(11y + 95)^\circ$, and $(4x - 2)^\circ$ with a transversal $t$. 2. **Identify angle relationships:** Since $l \parallel m$, alternate interior angles are equal. Thus, $$17x + 14 = 11y + 95$$ 3. **Use adjacent angle relationship:** Angles $(11y + 95)^\circ$ and $(4x - 2)^\circ$ are adjacent on line $m$, so they are supplementary: $$ (11y + 95) + (4x - 2) = 180 $$ 4. **Write the system of equations:** $$\begin{cases} 17x + 14 = 11y + 95 \\ 11y + 95 + 4x - 2 = 180 \end{cases}$$ Simplify second equation: $$11y + 4x + 93 = 180$$ $$11y + 4x = 87$$ 5. **Rewrite first equation:** $$17x + 14 = 11y + 95$$ $$17x - 11y = 81$$ 6. **Solve the system:** $$\begin{cases} 17x - 11y = 81 \\ 4x + 11y = 87 \end{cases}$$ Add equations to eliminate $y$: $$ (17x - 11y) + (4x + 11y) = 81 + 87 $$ $$ 21x = 168 $$ $$ x = \frac{168}{21} = 8 $$ 7. **Find $y$ by substituting $x=8$ into second equation:** $$4(8) + 11y = 87$$ $$32 + 11y = 87$$ $$11y = 87 - 32 = 55$$ $$y = \frac{55}{11} = 5$$ **Final answer:** $$x = 8, \quad y = 5$$