1. **Problem:** Find the value of $x$ in a triangle with angles $(2x+16)^\circ$, $80^\circ$, and $(x+1)^\circ$. 2. **Formula:** The sum of angles in any triangle is always $180^\circ$. 3. **Equation:** $$ (2x+16) + 80 + (x+1) = 180 $$ 4. **Simplify:** $$ 2x + 16 + 80 + x + 1 = 180 $$ $$ 3x + 97 = 180 $$ 5. **Solve for $x$:** $$ 3x = 180 - 97 $$ $$ 3x = 83 $$ $$ x = \frac{83}{3} = 27.67 $$ 6. **Check:** Angles are $2(27.67)+16 = 71.33^\circ$, $80^\circ$, and $27.67+1=28.67^\circ$. Sum: $71.33 + 80 + 28.67 = 180^\circ$ (correct). **Final answer:** $x = 27.67$ (approximately).