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 84° and 57°. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always 180°. This means: $$m\angle 1 + 84^\circ + 57^\circ = 180^\circ$$ 3. To find $m\angle 1$, subtract the sum of the known angles from 180°: $$m\angle 1 = 180^\circ - (84^\circ + 57^\circ)$$ 4. Calculate the sum inside the parentheses: $$84^\circ + 57^\circ = 141^\circ$$ 5. Subtract to find $m\angle 1$: $$m\angle 1 = 180^\circ - 141^\circ = 39^\circ$$ 6. Therefore, the measure of angle 1 is 39°.