1. **Problem Statement:** Given a quadrilateral with angles labeled as $d^\circ$, $c^\circ$, $(b - 10)^\circ$, and $(b + 10)^\circ$, solve for the variables $b$, $c$, and $d$. 2. **Formula and Rules:** The sum of interior angles in any quadrilateral is always $360^\circ$. 3. **Set up the equation:** $$d + c + (b - 10) + (b + 10) = 360$$ 4. **Simplify the equation:** Combine like terms: $$d + c + b - 10 + b + 10 = 360$$ $$d + c + 2b = 360$$ 5. **Explanation:** Without additional information about the relationships between $d$, $c$, and $b$, we cannot solve for each variable individually. However, this equation relates them. 6. **If the quadrilateral is a parallelogram or rectangle:** Opposite angles are equal, so: $$d = (b - 10)$$ $$c = (b + 10)$$ 7. **Substitute these into the sum equation:** $$d + c + (b - 10) + (b + 10) = (b - 10) + (b + 10) + (b - 10) + (b + 10) = 4b = 360$$ 8. **Solve for $b$:** $$4b = 360$$ $$\cancel{4}b = \cancel{4}90$$ $$b = 90$$ 9. **Find $d$ and $c$:** $$d = b - 10 = 90 - 10 = 80$$ $$c = b + 10 = 90 + 10 = 100$$ **Final answer:** $$b = 90^\circ, \quad d = 80^\circ, \quad c = 100^\circ$$