Final answer:
The angle pair name justifying the equation 2x + 160 = 3x - 40 is vertical angles, which are congruent angles formed by intersecting lines.
Step-by-step explanation:
The angle pair name that justifies the equation setup and solution for 2x + 160 = 3x - 40 is vertical angles. Vertical angles are formed when two lines intersect, creating two pairs of opposite angles that are congruent.
In this equation, we presume an intersection where the non-adjacent angles are equal, justifying the setup where the measures of the angles are expressed as 2x + 160 and 3x - 40.
When solving the given equation, we subtract 2x from each side to get 160 = x - 40. Then, we add 40 to both sides to find x, which would give us the measure of the angle once plugged back into either of the original expressions, thereby verifying that the angles are indeed vertical angles.