Question

given: lines a and b are parallel and line c is a transversal. prove: ∠2 is supplementary to ∠8 what is the missing reason in the proof? 1. ( aparallel b ), is a transv 1. given 2. ( angle6congangle2 ) 2. ? 3. ( mangle6 = mangle2 ) 3. def. of congruent 4. ( angle6 ) is supp. to ( angle8 ) 4. def. of linear pair 5. ( angle2 ) is supp. to ( angle8 ) 5. congruent supplements theorem

Explanation:

When two parallel lines are cut by a transversal, alternate exterior angles are congruent. In this case, line \(a\parallel b\) and line \(c\) is the transversal. \(\angle6\) and \(\angle2\) are alternate exterior angles. So, the reason for \(\angle6\cong\angle2\) is the alternate exterior angles theorem.

Answer:

alternate exterior angles theorem