1. **State the problem:** We need to find the measure of angle 1, denoted as $m \angle 1$, in a triangle where the other two angles are given as $108^\circ$ and $143^\circ$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always $180^\circ$. This means: $$m \angle 1 + 108^\circ + 143^\circ = 180^\circ$$ 3. **Calculate the sum of the known angles:** $$108^\circ + 143^\circ = 251^\circ$$ 4. **Find $m \angle 1$ by subtracting the sum of known angles from $180^\circ$:** $$m \angle 1 = 180^\circ - 251^\circ = -71^\circ$$ 5. **Interpretation:** Since the sum of the two given angles exceeds $180^\circ$, this is not possible for a triangle. Therefore, there might be an error in the given angle measures or the figure is not a triangle. **Final answer:** $m \angle 1$ cannot be determined as the given angles do not form a valid triangle.