1. **State the problem:** We are given a triangle with three angles labeled as $x^\circ$, $2x^\circ$, and $(x - 20)^\circ$. We need to write an equation modeling the sum of these angles and solve for $x$. Then, find the measures of each angle. 2. **Formula and rule:** The sum of the interior angles of any triangle is always $180^\circ$. So, $$x + 2x + (x - 20) = 180$$ 3. **Write the equation:** Combine like terms: $$x + 2x + x - 20 = 180$$ $$4x - 20 = 180$$ 4. **Solve for $x$:** Add 20 to both sides: $$4x - \cancel{20} + 20 = 180 + 20$$ $$4x = 200$$ Divide both sides by 4: $$\frac{4x}{\cancel{4}} = \frac{200}{\cancel{4}}$$ $$x = 50$$ 5. **Find each angle measure:** - First angle: $x = 50^\circ$ - Second angle: $2x = 2 \times 50 = 100^\circ$ - Third angle: $x - 20 = 50 - 20 = 30^\circ$ 6. **Check sum:** $$50 + 100 + 30 = 180^\circ$$ which confirms the solution is correct. **Final answer:** The angles measure $50^\circ$, $100^\circ$, and $30^\circ$.