1. **State the problem:** We have a triangle with three angles: $2x + 16$, $x + 1$, and $80$ degrees. We need to find the value of $x$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always $180^\circ$. 3. **Set up the equation:** $$ (2x + 16) + (x + 1) + 80 = 180 $$ 4. **Simplify the equation:** $$ 2x + 16 + x + 1 + 80 = 180 $$ $$ 3x + 97 = 180 $$ 5. **Solve for $x$:** $$ 3x = 180 - 97 $$ $$ 3x = 83 $$ $$ x = \frac{83}{3} \approx 27.67 $$ 6. **Check the solution:** Calculate each angle: - $2x + 16 = 2(27.67) + 16 = 55.34 + 16 = 71.34^\circ$ - $x + 1 = 27.67 + 1 = 28.67^\circ$ - $80^\circ$ (given) Sum: $71.34 + 28.67 + 80 = 180.01^\circ$ (rounding error), so the solution is correct. **Final answer:** $$ x = \frac{83}{3} \approx 27.67 $$