1. The problem asks us to find the value of $y$ such that the angle $2y + 12$ degrees is obtuse. 2. An angle is obtuse if it is greater than $90^\circ$ but less than $180^\circ$. 3. Set up the inequality: $$2y + 12 > 90$$ 4. Subtract 12 from both sides: $$2y > 78$$ 5. Divide both sides by 2: $$y > 39$$ 6. Now check which given options satisfy $y > 39$: - a. 5 (no) - b. 25 (no) - c. 15 (no) - d. 40 (yes) 7. Only option d. $y=40$ makes the angle obtuse: $$2(40) + 12 = 80 + 12 = 92^\circ$$ which is greater than $90^\circ$ and less than $180^\circ$. **Final answer:** d. 40