1. **Stating the problem:** We need to find the measure of angle 1, denoted as $m\angle 1$, in a triangle where two other angles are given: 34° and 113°. 2. **Formula used:** The sum of the interior angles in any triangle is always 180°. This is expressed as: $$m\angle 1 + 34^\circ + 113^\circ = 180^\circ$$ 3. **Calculate $m\angle 1$:** Subtract the sum of the known angles from 180°: $$m\angle 1 = 180^\circ - (34^\circ + 113^\circ)$$ 4. **Simplify the expression:** $$m\angle 1 = 180^\circ - 147^\circ = 33^\circ$$ 5. **Conclusion:** The measure of angle 1 is $33^\circ$. This method uses the fundamental property of triangles that their interior angles sum to 180°, allowing us to find the missing angle when the other two are known.