Final answer:
The correct value of x that would make corresponding angles congruent is 5. The property of corresponding angles in parallel lines dictates that they are congruent, hence the two equations set for these angles, when solved for x, should give a common value which, in this case, is 5.
Step-by-step explanation:
When a set of parallel lines are cut by a transversal, corresponding angles are angles that are in the same position relative to each parallel line and the transversal. By definition, corresponding angles are congruent when the lines are parallel. In the given problem, angles 2 and 6 are corresponding angles, and so they should have equal measures if the lines are indeed parallel.
The equations given for m<2 and m<6 are m<2 = (7x - 5) and m<6 = (x + 25) respectively. To find the value of x that would make these angles congruent, we set the two expressions equal to each other and solve for x:
7x - 5 = x + 25
Simplifying, we subtract x from both sides and add 5 to both sides:
6x = 30
Therefore, x = 5.
This means that the correct answer is A: x = 5. Corresponding angles are congruent, and setting x to 5 ensures these angles have the same measure, demonstrating the property of corresponding angles when lines are cut by a transversal.