1. **State the problem:** Find the missing angle measure $m\angle J$ in triangle KLM where $m\angle L = 118^\circ$ and $m\angle M = 130^\circ$. 2. **Recall the angle sum property of triangles:** The sum of interior angles in any triangle is always $180^\circ$. 3. **Set up the equation:** $$m\angle J + m\angle L + m\angle M = 180^\circ$$ 4. **Substitute known values:** $$m\angle J + 118^\circ + 130^\circ = 180^\circ$$ 5. **Simplify the sum of known angles:** $$m\angle J + 248^\circ = 180^\circ$$ 6. **Isolate $m\angle J$ by subtracting $248^\circ$ from both sides:** $$m\angle J = 180^\circ - 248^\circ$$ 7. **Calculate the result:** $$m\angle J = -68^\circ$$ 8. **Interpretation:** A negative angle measure is not possible in this context, indicating the given angles cannot form a triangle. There may be an error in the given angle measures or the figure is not a triangle. **Final answer:** $m\angle J$ cannot be determined as the given angles do not form a valid triangle.