1. The problem asks for the measure of angle 1 ($m \angle 1$) in a triangle where the other two angles are $36^\circ$ and $96^\circ$. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always $180^\circ$. 3. Using the theorem, we write the equation: $$m \angle 1 + 36^\circ + 96^\circ = 180^\circ$$ 4. Combine the known angles: $$36^\circ + 96^\circ = 132^\circ$$ 5. Substitute back: $$m \angle 1 + 132^\circ = 180^\circ$$ 6. Solve for $m \angle 1$: $$m \angle 1 = 180^\circ - 132^\circ = 48^\circ$$ 7. Therefore, the measure of angle 1 is $48^\circ$.