1. The problem is to find the value of angle $x$ in a triangle where the other two angles are $115^\circ$ and $35^\circ$. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always $180^\circ$. 3. Using the theorem, we write the equation: $$115^\circ + 35^\circ + x = 180^\circ$$ 4. Simplify the sum of the known angles: $$150^\circ + x = 180^\circ$$ 5. Solve for $x$ by subtracting $150^\circ$ from both sides: $$x = 180^\circ - 150^\circ = 30^\circ$$ 6. Therefore, the value of angle $x$ is $30^\circ$.