1. The problem asks for the measure of angle 1 in a triangle where the other two angles are 143° and 34°. 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: $$143° + 34° + m\angle 1 = 180°$$ 4. Add the known angles: $$177° + m\angle 1 = 180°$$ 5. Subtract 177° from both sides to isolate $m\angle 1$: $$m\angle 1 = 180° - 177°$$ 6. Calculate the difference: $$m\angle 1 = 3°$$ 7. Therefore, the measure of angle 1 is 3°.