1. **State the problem:** We are given a triangle with three angles labeled $x^\circ$, $2x^\circ$, and $(x - 20)^\circ$. We need to write an equation that models the sum of these angles. 2. **Recall the rule:** The sum of the measures of the angles in any triangle is always $180^\circ$. This is a fundamental property of triangles. 3. **Write the equation:** Using the given angles, the sum is: $$x + 2x + (x - 20) = 180$$ 4. **Simplify the equation:** Combine like terms: $$x + 2x + x - 20 = 180$$ $$4x - 20 = 180$$ 5. **Solve for $x$:** Add 20 to both sides: $$4x - 20 + 20 = 180 + 20$$ $$4x = 200$$ 6. **Divide both sides by 4:** $$\frac{\cancel{4}x}{\cancel{4}} = \frac{200}{4}$$ $$x = 50$$ 7. **Interpret the result:** The value of $x$ is $50^\circ$. This means the angles are: - $x = 50^\circ$ - $2x = 100^\circ$ - $x - 20 = 30^\circ$ 8. **Check the sum:** $$50 + 100 + 30 = 180$$ The sum is correct, confirming our solution. **Final answer:** $x = 50^\circ$