Question

select the correct answer.
given: line l and line m intersect
prove: ∠1 ≅ ∠3
which statement and reason best completes the proof?
statements\treasons

1. line l and line m intersect\t1. given
2. ∠1 is supplementary to ∠2\t2. linear pair theorem

3.?\t3.?

1. ∠1 ≅ ∠3\t4. congruent supplements theorem

a. 3 m∠1 + m∠2 = 180°\t3. definition of supplementary angles
b. 3 ∠3 is supplementary to ∠2\t3. linear pair theorem
c. 3 m∠1 + m∠3 = 180°\t3. definition of supplementary angles
d. 3 ∠1 is supplementary to ∠4\t3. linear pair theorem

Explanation:

Step1: Identify linear pair for $\angle2$

$\angle2$ and $\angle3$ form a linear pair.

Step2: Apply linear pair theorem

By linear pair theorem, $m\angle2 + m\angle3 = 180^\circ$, so $\angle3$ is supplementary to $\angle2$.

Step3: Align with proof structure

This fills the missing statement/reason, leading to using congruent supplements theorem to prove $\angle1\cong\angle3$.

Answer:

B. 3. $\angle 3$ is supplementary to $\angle 2$

1. linear pair theorem