1. The problem asks to find the measure of angle 1 ($m\angle 1$) in a triangle where the other two angles are given as 141° and 51°. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always 180°. 3. Using the theorem, we write the equation: $$141^\circ + 51^\circ + m\angle 1 = 180^\circ$$ 4. Add the known angles: $$192^\circ + m\angle 1 = 180^\circ$$ 5. Solve for $m\angle 1$ by subtracting 192° from both sides: $$m\angle 1 = 180^\circ - 192^\circ = -12^\circ$$ 6. Since an angle in a triangle cannot be negative, this indicates an error in the given angle measures; the sum of 141° and 51° already exceeds 180°, which is impossible for a triangle. 7. Therefore, the problem as stated is invalid because the angles do not form a triangle. Final answer: The given angles cannot form a triangle, so $m\angle 1$ is undefined.