Question

Using the theorems and given information, which of the following proves a∥b

?

Given: m∠2=(6x+28)∘
, m∠6=(11x−7)∘
, and x=7
The figure shows two lines a and b, cut by the transversal. The intersection of line a and the transversal forms four angles, the top right angle is labeled as two, the bottom right angle is labeled as three, the bottom left angle is labeled as four, and the top left angle is labeled as one. The intersection of line b and the transversal forms four angles, the top right angle is labeled as six, the bottom right angle is labeled as seven, the bottom left angle is labeled as eight, and the top left angle is labeled as five.

Answer 1

Based on the given information, we can use the Alternate Interior Angles Theorem to prove that lines a and b are parallel. The theorem states that if a transversal intersects two parallel lines, then the alternate interior angles are congruent. In this case, we have m∠2 = (6x + 28)° and m∠6 = (11x - 7)°, where x = 7. By substituting x = 7 into the equations, we find that m∠2 = 70° and m∠6 = 70°. Since the alternate interior angles are congruent, we can conclude that lines a and b are parallel.