1. The problem asks to find the measure of angle 1 (m\angle 1) in a triangle where the other two angles are 113° and 74°. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always 180°. This means: $$m\angle 1 + 113^\circ + 74^\circ = 180^\circ$$ 3. Substitute the known values and solve for $m\angle 1$: $$m\angle 1 = 180^\circ - 113^\circ - 74^\circ$$ 4. Calculate the right side: $$m\angle 1 = 180^\circ - 187^\circ = -7^\circ$$ 5. Since an angle cannot be negative, check the sum of the given angles: $113^\circ + 74^\circ = 187^\circ$, which is already greater than 180°, so the given angles cannot form a triangle. There might be an error in the problem's given angle measures. 6. If the problem intended the angles to be 113° and 47° (instead of 74°), then: $$m\angle 1 = 180^\circ - 113^\circ - 47^\circ = 20^\circ$$ 7. Please verify the given angle measures. If the angles are correct as 113° and 74°, then no triangle can be formed. Final answer: The given angles do not form a valid triangle, so $m\angle 1$ cannot be determined with the provided information.