1. The problem asks for the measure of angle 1, denoted as $m\angle 1$, in a triangle where the other two angles are given as $101^\circ$ and $35^\circ$. 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: $$m\angle 1 + 101^\circ + 35^\circ = 180^\circ$$ 4. Combine the known angles: $$m\angle 1 + 136^\circ = 180^\circ$$ 5. Subtract $136^\circ$ from both sides to isolate $m\angle 1$: $$m\angle 1 = 180^\circ - 136^\circ$$ 6. Calculate the difference: $$m\angle 1 = 44^\circ$$ 7. Therefore, the measure of angle 1 is $44^\circ$.