Question

Solve for x to make A||B.
A
B
5x
3x + 20
x = [?]

Answer 1

To solve for x and make line A parallel to line B, we use the property that corresponding angles are equal when a transversal intersects parallel lines. In this case, we can set up an equation by equating the expressions for corresponding angles. The angles formed by the intersection of line A and the transversal are represented by 5x, and those on line B are represented by 3x + 20. Thus, we have:

`\[5x = 3x + 20\]`

To isolate x, we can subtract 3x from both sides:

`\[2x = 20\]`

Now, divide both sides by 2:

`\[x = 10\]`

Therefore, for lines A and B to be parallel, x must equal 10. This ensures that the corresponding angles are equal, satisfying the condition for parallel lines.