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 measure 144° and 104°. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always 180°. This means: $$m\angle 1 + 144^\circ + 104^\circ = 180^\circ$$ 3. **Set up the equation:** $$m\angle 1 = 180^\circ - 144^\circ - 104^\circ$$ 4. **Calculate the value:** $$m\angle 1 = 180^\circ - 248^\circ = -68^\circ$$ 5. **Interpretation:** Since the sum of the two given angles exceeds 180°, this cannot form a valid triangle with angle 1 positive. Therefore, the given angle measures are inconsistent for a triangle. **Final answer:** The given angles cannot form a triangle, so $m\angle 1$ is undefined or does not exist under these conditions.