1. The problem asks to find the missing angle $x$ in a triangle where the other two angles are $85^\circ$ and $45^\circ$. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always $180^\circ$. 3. Using the formula: $$x + 85^\circ + 45^\circ = 180^\circ$$ 4. Combine the known angles: $$x + 130^\circ = 180^\circ$$ 5. Subtract $130^\circ$ from both sides to isolate $x$: $$x = 180^\circ - 130^\circ$$ 6. Calculate the difference: $$x = 50^\circ$$ 7. Therefore, the missing angle $x$ is $50^\circ$. This is because the sum of all angles in a triangle must be $180^\circ$, so subtracting the sum of the known angles from $180^\circ$ gives the missing angle.