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? statement reason 1. a || b, c is a transversal 1. given 2. ∠6 ≅ ∠2 2. ? 3. m∠6 = m∠2 3. def. of congruent 4. ∠6 is supp. to ∠8 4. def. of linear pair 5. ∠2 is supp. to ∠8 5. congruent supplements theorem corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem

Explanation:

Step1: Analyze each theorem

• Corresponding angles theorem: States that if two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. But ∠6 and ∠2 are not in corresponding positions.
• Alternate interior angles theorem: Applies to angles between the two parallel lines. ∠6 and ∠2 are not alternate interior angles.
• Vertical angles theorem: Deals with angles opposite each other when two lines intersect. Not relevant here.
• Alternate exterior angles theorem: When two parallel lines are cut by a transversal, alternate exterior angles are congruent. ∠2 and ∠6 are alternate exterior angles.

Answer:

alternate exterior angles theorem