1. **State the problem:** We need to find the value of angle $x$ in a triangle where the other two angles are $60^\circ$ and $50^\circ$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always $180^\circ$. 3. **Set up the equation:** $$x + 60 + 50 = 180$$ 4. **Simplify the equation:** $$x + 110 = 180$$ 5. **Isolate $x$ by subtracting 110 from both sides:** $$x = 180 - 110$$ 6. **Calculate the value:** $$x = 70$$ **Final answer:** The value of $x$ is $70^\circ$.