1. **State the problem:** We need to find the measure of angle 1, denoted as $m\angle 1$, in a triangle where two angles are given as $30^\circ$ and $119^\circ$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always $180^\circ$. This means: $$m\angle 1 + 30^\circ + 119^\circ = 180^\circ$$ 3. **Set up the equation:** $$m\angle 1 = 180^\circ - 30^\circ - 119^\circ$$ 4. **Calculate:** $$m\angle 1 = 180^\circ - 149^\circ = 31^\circ$$ 5. **Conclusion:** The measure of angle 1 is $31^\circ$.