1. The problem is to find the value of the angle $x$ in a triangle where the other two angles are $120^\circ$ and $35^\circ$. 2. The key formula to use is the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always $180^\circ$: $$x + 120 + 35 = 180$$ 3. We substitute the known angles into the equation: $$x + 120 + 35 = 180$$ 4. Simplify the sum of the known angles: $$x + 155 = 180$$ 5. To isolate $x$, subtract $155$ from both sides: $$x + \cancel{155} - \cancel{155} = 180 - 155$$ 6. Simplify the right side: $$x = 25$$ 7. Therefore, the value of $x$ is $25^\circ$. This matches the equation $x + 120 + 35 = 180$ from the options given, which is the correct equation to find $x$.