1. **State the problem:** Given two parallel lines $m \parallel n$ cut by a transversal, find the values of $x$ and $y$ given the angles $(y + 16)^\circ$, $(3x - 15)^\circ$, and $(2x + 7)^\circ$. 2. **Recall the rules:** When two parallel lines are cut by a transversal, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary. 3. **Identify angle relationships:** The angle $(y + 16)^\circ$ is corresponding to $(2x + 7)^\circ$ because they are on the same side of the transversal and in corresponding positions. Therefore, $$y + 16 = 2x + 7$$ 4. The angles $(3x - 15)^\circ$ and $(2x + 7)^\circ$ are consecutive interior angles on the same side of the transversal, so they are supplementary: $$ (3x - 15) + (2x + 7) = 180 $$ 5. **Solve the system:** From the first equation: $$ y + 16 = 2x + 7 $$ $$ y = 2x + 7 - 16 $$ $$ y = 2x - 9 $$ From the second equation: $$ 3x - 15 + 2x + 7 = 180 $$ $$ 5x - 8 = 180 $$ $$ 5x = 188 $$ $$ x = \frac{188}{5} = 37.6 $$ 6. Substitute $x$ back to find $y$: $$ y = 2(37.6) - 9 = 75.2 - 9 = 66.2 $$ **Final answer:** $$ x = 37.6, \quad y = 66.2 $$