1. **State the problem:** We need to find the measure of angle 1 in a triangle where the other two angles are 136° and 87°. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always 180°. This means: $$m \angle 1 + 136^\circ + 87^\circ = 180^\circ$$ 3. **Set up the equation:** $$m \angle 1 = 180^\circ - 136^\circ - 87^\circ$$ 4. **Calculate:** $$m \angle 1 = 180^\circ - 223^\circ = -43^\circ$$ 5. **Interpretation:** Since the sum of the two given angles exceeds 180°, this is not possible for a triangle. There might be an error in the given angle measures or the figure is not a triangle. **Final answer:** The given angles cannot form a triangle, so $m \angle 1$ is undefined with the provided data.