Question

3 complete the proof.
given: k || l
prove: ∠1 and ∠6 are supplementary
statements reasons

1. k || l 1. given
2. ∠1 ≅ ∠7 2. ??
3. m∠1 = m∠7 3. definition of congruence
4. ∠7 and ∠6 are supplementary 4. linear pair theorem
5. m∠7 + m∠6 = 180° 5. definition of supplementary angles
6. m∠1 + m∠6 = 180° 6. substitution
7. ∠1 and ∠6 are supplementary 7. definition of supplementary angles

select the missing reason for
a alternate exterior angles theorem
b alternate interior angles theorem
c same - side interior angles theorem
d corresponding angles theorem

Explanation:

$\angle1$ and $\angle7$ are alternate exterior angles formed by two parallel lines $k$ and $l$ and a transversal. According to the Alternate Exterior Angles Theorem, when two parallel lines are cut by a transversal, alternate exterior angles are congruent.

Answer:

A. Alternate Exterior Angles Theorem