1. **Problem:** Find the value of $x$ given the angles $(x - 5)^\circ$, $(2x - 7)^\circ$, and $21^\circ$ in a triangle. 2. **Formula:** The sum of interior angles in a triangle is always $180^\circ$. 3. **Set up the equation:** $$ (x - 5) + (2x - 7) + 21 = 180 $$ 4. **Simplify the equation:** $$ x - 5 + 2x - 7 + 21 = 180 $$ $$ 3x + 9 = 180 $$ 5. **Isolate $x$:** $$ 3x = 180 - 9 $$ $$ 3x = 171 $$ 6. **Divide both sides by 3:** $$ \cancel{3}x = \frac{171}{\cancel{3}} $$ $$ x = 57 $$ **Final answer:** $x = 57$