Question

1. line a and line b intersect 1 given

2? 2?

1. ∠3 is supplementary to ∠2 3. linear pair theorem
2. ∠1 ≅ ∠3 4. congruent supplements theorem

which statement and reason best completes the proof?
a. 2 ∠2 is supplementary to ∠4 2. linear pair theorem
b. 2 m∠2 + m∠3 = 180° 2. definition of supplementary angles
c. 2 ∠1 is supplementary to ∠2 2. linear pair theorem
d. 2 m∠1 + m∠4 = 180° 2. definition of supplementary angles

Explanation:

Step1: Analyze proof flow

We need a statement/reason that sets up using the congruent supplements theorem (step 4), which requires ∠1 and ∠3 to both be supplementary to ∠2.

Step2: Evaluate option alignment

Step 3 states ∠3 is supplementary to ∠2. To use the congruent supplements theorem, we need ∠1 to also be supplementary to ∠2, which comes from the linear pair theorem (∠1 and ∠2 form a linear pair).

Step3: Match to correct option

Option C provides the required statement and valid reason that connects to the given proof steps.

Answer:

C. 2. ∠1 is supplementary to ∠2

1. linear pair theorem