1. **State the problem:** Solve the equation $x - 2x + 17 = -2x + 17 = 180^\circ$ for $x$. 2. **Rewrite the equation:** The problem gives two expressions: $$x - 2x + 17 = -2x + 17 = 180^\circ$$ This means: $$x - 2x + 17 = 180^\circ$$ 3. **Simplify the left side:** $$x - 2x + 17 = (1x - 2x) + 17 = -x + 17$$ So the equation becomes: $$-x + 17 = 180^\circ$$ 4. **Isolate $x$:** Subtract 17 from both sides: $$-x + 17 - 17 = 180^\circ - 17$$ $$-x = 163^\circ$$ Multiply both sides by $-1$: $$\cancel{-}x \times \cancel{-1} = 163^\circ \times (-1)$$ $$x = -163^\circ$$ 5. **Check your answer:** Substitute $x = -163^\circ$ back into the original expression: $$x - 2x + 17 = -163 - 2(-163) + 17 = -163 + 326 + 17 = 180^\circ$$ This confirms the solution is correct. **Final answer:** $$x = -163^\circ$$