1. **State the problem:** We need to find the measure of the smallest angle in a triangular pond where the interior angles are given as $(2y - 4)^\circ$, $(y + 7)^\circ$, and $(3y + 14)^\circ$. 2. **Recall the rule:** The sum of the interior angles of any triangle is always $180^\circ$. 3. **Set up the equation:** $$ (2y - 4) + (y + 7) + (3y + 14) = 180 $$ 4. **Simplify the equation:** $$ 2y - 4 + y + 7 + 3y + 14 = 180 $$ $$ (2y + y + 3y) + (-4 + 7 + 14) = 180 $$ $$ 6y + 17 = 180 $$ 5. **Solve for $y$:** $$ 6y = 180 - 17 $$ $$ 6y = 163 $$ $$ y = \frac{163}{6} \approx 27.17 $$ 6. **Find each angle:** - First angle: $2y - 4 = 2(27.17) - 4 = 54.34 - 4 = 50.34^\circ$ - Second angle: $y + 7 = 27.17 + 7 = 34.17^\circ$ - Third angle: $3y + 14 = 3(27.17) + 14 = 81.51 + 14 = 95.51^\circ$ 7. **Identify the smallest angle:** The smallest angle is approximately $34.17^\circ$. **Final answer:** Smallest angle = $34.17$ degrees