1. The problem asks for the measure of angle $\angle 1$ in a triangle where two other angles are given as $31^\circ$ and $79^\circ$. 2. Recall that the sum of the interior angles in any triangle is always $180^\circ$. 3. Use the formula for the sum of angles in a triangle: $$\angle 1 + 31^\circ + 79^\circ = 180^\circ$$ 4. Combine the known angles: $$31^\circ + 79^\circ = 110^\circ$$ 5. Substitute back into the equation: $$\angle 1 + 110^\circ = 180^\circ$$ 6. Solve for $\angle 1$: $$\angle 1 = 180^\circ - 110^\circ = 70^\circ$$ 7. Therefore, the measure of $\angle 1$ is $70^\circ$.