Answer:
A. 2. ∡1 is supplementary to ∡2 (linear pair theorem)
Step-by-step explanation:
Given the following proof so far, we have:
1. Line a and line b intersect => given
2. ? => ?
3. ∡3 is supplementary to ∡2 => linear pair theorem
4. ∡1 ≅ ∡3 => congruent supplements theorem
Now let's take a look at the reasoning for statement 4, which says that angle 1 and 3 are congruent due to congruent supplements theorem.
In this theorem, if 2 angles are supplementary (add up to 180 degrees) to the same angle, it means those 2 angles are congruent.
Why does this work?
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Let's say x + y = 180, and z + y = 180
By transitivity (if a = b and b =c, then a=c), x + y is equal to z + y
x + y = z + y
Subtract y from both sides
x = z
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Statement 3 says ∡3 is supplementary to ∡2, and because of congruent supplements theorem being our last reason (where ∡1 and ∡3 are congruent), we need to make statement 2 also have ∡1 being supplementary to ∡2, (∡2 is like y in the example above - it's the angle that ∡1 and ∡3 are both supplementary to).
This will eliminate choices B (which has ∡1, but also ∡4 which isn't necessary), C ( ∡which mentions nothing about ∡1), and D (which also doesn't mention anything about ∡1, and which also isn't necessary as we have statement 3 essentially saying the same thing), leaving A as the correct answer.
