1. The problem asks us to find the value of angle $x$ in a triangle where the other two angles are $31^\circ$ and $108^\circ$. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always $180^\circ$. 3. Using this theorem, we write the equation: $$x + 31^\circ + 108^\circ = 180^\circ$$ 4. Combine the known angles: $$31^\circ + 108^\circ = 139^\circ$$ 5. Substitute back into the equation: $$x + 139^\circ = 180^\circ$$ 6. Solve for $x$ by subtracting $139^\circ$ from both sides: $$x = 180^\circ - 139^\circ = 41^\circ$$ 7. Therefore, the value of $x$ is $41^\circ$.