1. The problem asks to find the measure of angle 1 (m\angle 1) in a triangle where two angles are given: 31° and 119°. 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: $$31^\circ + 119^\circ + m\angle 1 = 180^\circ$$ 4. Add the known angles: $$150^\circ + m\angle 1 = 180^\circ$$ 5. Subtract 150° from both sides to isolate m\angle 1: $$m\angle 1 = 180^\circ - 150^\circ = 30^\circ$$ 6. Therefore, the measure of angle 1 is 30°.