1. The problem asks to find the measure of angle 1, denoted as $m\angle 1$, in a triangle where the other two angles are given as 147° and 116°. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always 180°. 3. Using the theorem, we write the equation: $$147^\circ + 116^\circ + m\angle 1 = 180^\circ$$ 4. Add the known angles: $$147 + 116 = 263$$ 5. Substitute back: $$263 + m\angle 1 = 180$$ 6. To find $m\angle 1$, subtract 263 from both sides: $$m\angle 1 = 180 - 263 = -83$$ 7. Since an angle in a triangle cannot be negative, this indicates the given angles cannot form a triangle. The sum of the two given angles already exceeds 180°, so $m\angle 1$ does not exist in this context. Final answer: The given angles 147° and 116° cannot form a triangle with a third angle $m\angle 1$ because their sum exceeds 180°.