Question

given: line a and line b intersect
prove: ∠1≅∠3
statements reasons

1. line a and line b intersect 1. given
2. ? 2. ?
3. ∠3 is supplementary to ∠2 3. linear - pair theorem
4. ∠1≅∠3 4. congruent supplements theorem

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

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are adjacent and supplementary. Since line a and line b intersect, ∠1 and ∠2 form a linear pair.

Step2: Apply linear - pair theorem

By the linear - pair theorem, if two angles form a linear pair, they are supplementary. So, ∠1 is supplementary to ∠2.

Answer:

D. 2. ∠1 is supplementary to ∠2; 2. linear pair theorem