1. **Problem:** Find $x$ in the equation $$105^\circ + x^\circ + 40^\circ + 75^\circ = 360^\circ$$ 2. **Formula:** The sum of angles around a point is always $$360^\circ$$. 3. **Step 1:** Add the known angles: $$105 + 40 + 75 = 220$$ 4. **Step 2:** Set up the equation for $x$: $$220 + x = 360$$ 5. **Step 3:** Solve for $x$: $$x = 360 - 220$$ $$x = 140$$ 6. **Answer:** The missing angle $x$ is $$140^\circ$$. --- For the other angle measures in the first problem, the angles are: - $105^\circ$ - $140^\circ$ - $40^\circ$ - $75^\circ$ Since the user asked for the first problem only, this completes the solution. **Summary:** - The sum of angles around a point is $360^\circ$. - Add known angles and subtract from $360^\circ$ to find the missing angle.