Since line n intersects lines l and m, forming the angles shown in the diagram below, a value of x that would prove l || m is: B. 4.5.
In Mathematics and Geometry, the alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent:
By applying the alternate interior angles theorem to parallel lines l and m cut through by transversal n, we can reasonably infer and logically deduce the following pair of congruent angles;
6x + 42 = 18x - 12
18x - 6x = 42 + 12
12x = 54
x = 54/12
x = 4.5
Complete Question:
Line n intersects lines l and m, forming the angles shown in the diagram below.
Which value of x would prove l || m?
A. 8.75
B. 4.5
C. 2.5
D. 3.7