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If m<3 = (4x + 38)° and m<5 = (6x – 10°)
what value of x proves r || s?

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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.

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