To determine the value of x that makes lines l and m parallel, we apply the property that states the corresponding angles formed when a transversal intersects two parallel lines are equal.
Assuming there are angles formed at the intersection of lines l, m, and the transversal, we first identify these angles. Let’s say angle A is one angle formed at line l, and angle B is the corresponding angle at line m. For lines l and m to be parallel, we must have:
Angle A = Angle B
We can express these angles in terms of x. For example, if:
– Angle A = 2x + 10
– Angle B = 3x – 5
Setting them equal gives us the equation:
2x + 10 = 3x – 5
Next, we solve for x:
Step 1: Subtract 2x from both sides:
10 = x – 5
Step 2: Add 5 to both sides:
15 = x
Thus, the value of x that makes lines l and m parallel is x = 15.
In summary, by using the relationship between the angles formed by a transversal and parallel lines, we determined the necessary value of x for the two lines to maintain parallelism.