Question

given: lines a and b are parallel and line c is a transversal. prove: ∠2 is supplementary to ∠8. 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:

Angle 2 and angle 6 are non - adjacent angles that lie on the inner side of the parallel lines a and b and on the opposite sides of the transversal c. By the alternate interior angles theorem, when two parallel lines are cut by a transversal, alternate interior angles are congruent. So, ∠6≅∠2.

Answer:

alternate interior angles theorem