Final answer:
To prove lines r and s are parallel, set the expressions for m<3 and m<5 equal, since they are corresponding angles, and solve for x to find that x equals 24.
Step-by-step explanation:
To determine the value of x that proves r is parallel to s (r || s), we need to use the concept of corresponding angles formed when a transversal intersects two parallel lines. Given the expressions for m<3 and m<5, we can set these equal to each other if the angles are corresponding: (4x + 38)° = (6x - 10)°. Solving this equation will allow us to find the value of x.
We can rearrange the equation: 38° + 10° = 6x - 4x, simplifying to 48° = 2x. Dividing by 2, we find x = 24, which is the value of x that confirms r || s due to the corresponding angles being equal, validating the parallel lines.