1. **Problem:** Find $x$ and the missing angle when two parallel lines are cut by a transversal, with angles $100^\circ$ and $(x+10)^\circ$ on the same side exterior. 2. **Formula and rule:** Same side exterior angles are supplementary, so their measures add up to $180^\circ$. 3. **Set up the equation:** $$x + 10 = 180$$ 4. **Solve for $x$:** $$x = 180 - 10$$ $$x = 170$$ 5. **Find the missing angle:** The missing angle is $(x+10)^\circ = 170 + 10 = 180^\circ$. 6. **Explanation:** Since same side exterior angles are supplementary, their sum is $180^\circ$. We used this property to set up the equation and solve for $x$. Then, substituting $x$ back gave the missing angle. **Final answer:** $$x = 170$$ Missing angle = $180^\circ$