Find the value of [tex]x[/tex] that makes [tex]m \parallel n[/tex].

Two parallel lines, [tex]m[/tex] and [tex]n[/tex], are cut by a transversal. Above the transversal, to the right of the first parallel line [tex]m[/tex], the angle is [tex]x[/tex] degrees. Above the transversal, to the left of the second parallel line [tex]n[/tex], the angle is [tex]2x[/tex] degrees.

Question

18-11-2023
Mathematics

High School

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Find the value of [tex]x[/tex] that makes [tex]m \parallel n[/tex].

Two parallel lines, [tex]m[/tex] and [tex]n[/tex], are cut by a transversal. Above the transversal, to the right of the first parallel line [tex]m[/tex], the angle is [tex]x[/tex] degrees. Above the transversal, to the left of the second parallel line [tex]n[/tex], the angle is [tex]2x[/tex] degrees.

Answer :

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lakshmimse20 lakshmimse20 · Answer 1 · 2024-04-29T16:30:46-04:00

Final answer:

When two parallel lines are cut by a transversal, the corresponding angles are equal. In this scenario, the angles are x degrees and 2x degrees. Solving for x in the equation x = 2x results in x = 0 degrees, which means the value of x that makes the lines m and n parallel is 0 degrees.

Explanation:

In geometry, when two parallel lines are cut by a transversal, the corresponding angles are equal. In this case, the pair of corresponding angles are x degrees (angle above the transversal on the right of line m) and 2x degrees (angle above the transversal on the left of line n). Since these two angles are corresponding angles, they should be equal for lines m and n to be parallel.

So, we form an equation with these angles: x = 2x.

To solve this equation, subtract x from both sides to isolate x:

x - x = 2x - x which simplifies to 0 = x,

Therefore, the value of x that makes the lines m and n parallel is 0 degrees.

Learn more about Parallel Lines and Transversals here:

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