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 $45^\circ$ and $79^\circ$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always $180^\circ$. This means: $$m \angle 1 + 45^\circ + 79^\circ = 180^\circ$$ 3. **Set up the equation:** $$m \angle 1 = 180^\circ - 45^\circ - 79^\circ$$ 4. **Calculate the value:** $$m \angle 1 = 180^\circ - 124^\circ = 56^\circ$$ 5. **Conclusion:** The measure of angle 1 is $56^\circ$. This is because the sum of all angles in a triangle must be $180^\circ$, so subtracting the known angles from $180^\circ$ gives the unknown angle.