1. **State the problem:** We need to find the measure of angle 1, denoted as $m\angle 1$, in a triangle where the other two angles are given as $95^\circ$ and $32^\circ$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always $180^\circ$. This means: $$m\angle 1 + 95^\circ + 32^\circ = 180^\circ$$ 3. **Set up the equation:** $$m\angle 1 = 180^\circ - 95^\circ - 32^\circ$$ 4. **Calculate:** $$m\angle 1 = 180^\circ - 127^\circ = 53^\circ$$ 5. **Conclusion:** The measure of angle 1 is $53^\circ$.