1. The problem is to find the value of angle $x$ in a triangle where the other two angles are $130^\circ$ and $55^\circ$. 2. Recall the rule that the sum of the interior angles of any triangle is always $180^\circ$. 3. Using the formula for the sum of angles in a triangle: $$130 + 55 + x = 180$$ 4. Add the known angles: $$185 + x = 180$$ 5. To isolate $x$, subtract $185$ from both sides: $$x = 180 - 185$$ 6. Simplify the right side: $$x = -5$$ 7. Since an angle in a triangle cannot be negative, this indicates an error in the given angles. The sum of $130^\circ$ and $55^\circ$ already exceeds $180^\circ$, so no valid triangle can have these angles. Final answer: No valid value for $x$ because the given angles do not form a triangle.