1. The problem involves finding the measure of angle $\angle 1$ in a right triangle where one angle is $90^\circ$ and another is $40^\circ$. 2. Recall that the sum of angles in any triangle is always $180^\circ$. 3. Since one angle is $90^\circ$ (right angle), and another is $40^\circ$, we can find $\angle 1$ by subtracting these from $180^\circ$: $$\angle 1 = 180^\circ - 90^\circ - 40^\circ$$ 4. Calculate the value: $$\angle 1 = 180^\circ - 130^\circ = 50^\circ$$ 5. Therefore, the measure of $\angle 1$ is $50^\circ$. This uses the fundamental property of triangle angles summing to $180^\circ$ and the given angle measures.