1. **State the problem:** We are given a triangle with two known angles: 42° and 47°, and we need to find the measure of the third angle, labeled as $m\angle 1$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always 180°. This means: $$m\angle 1 + 42^\circ + 47^\circ = 180^\circ$$ 3. **Set up the equation:** $$m\angle 1 = 180^\circ - 42^\circ - 47^\circ$$ 4. **Calculate:** $$m\angle 1 = 180^\circ - 89^\circ = 91^\circ$$ 5. **Conclusion:** The measure of angle 1 is $91^\circ$. This is because the sum of all angles in a triangle must be 180°, so subtracting the known angles from 180° gives the unknown angle.