To accurately support the fourth statement in the given proof, let's follow the reasoning step-by-step:
1. [tex]$\angle 1$[/tex] and [tex]$\angle 2$[/tex] form a linear pair.
- Reasoning: This is given in the problem.
2. [tex]$\angle ABC$[/tex] is a straight angle.
- Reasoning: If two angles form a linear pair, then they form a straight angle. This follows from the definition of a linear pair.
3. [tex]$\angle ABC = 180^{\circ}$[/tex].
- Reasoning: If an angle is a straight angle, then it measures [tex]$180^{\circ}$[/tex]. This is given by the definition of a straight angle.
4. [tex]$m\angle 1 + m\angle 2 = m\angle ABC$[/tex].
- Reasoning: The correct reason for this statement is the Angle Addition Postulate. The Angle Addition Postulate states that if a point lies in the interior of an angle, then the measure of the whole angle is equal to the sum of the measures of the two individual angles. In this case, [tex]$\angle ABC$[/tex] is the whole straight angle, and [tex]$\angle 1$[/tex] and [tex]$\angle 2$[/tex] are its parts. Hence, their measures add up to the measure of [tex]$\angle ABC$[/tex].
So, the reason that correctly supports the fourth statement is the Angle Addition Postulate.
