Note: Your teacher will grade your response to ensure you receive proper credit for your answers. Which solution for the value of x in the figure below is incorrect? Explain. The angle adjacent below the top parallel line and adjacent right to the transversal is labeled left parenthesis 4 x minus 2 right parenthesis degrees. The angle adjacent above the lower parallel line and adjacent left to the transversal is labeled left parenthesis 3 x plus 6 right parenthesis degrees.
A. 4x – 2 = 3x + 6
B. 4x – 2 + 3x + 6 = 180 x = 8 7x + 4 = 180 x = 25.1
The incorrect solution is option B.
Option A states that 4x - 2 = 3x + 6, which can be simplified to x = 8. This solution is correct.
However, in option B, the equation 4x - 2 + 3x + 6 = 180 is incorrect. The correct equation to represent the sum of the two angles adjacent to the transversal should be 4x - 2 + 3x + 6 = 180. By solving this equation, we get 7x + 4 = 180, which can be simplified to x = 25.1. This solution is incorrect because it does not satisfy the original equation given in option A (4x - 2 = 3x + 6).
The incorrect solution is B.
In solution B, the equation is set up as (4x - 2) + (3x + 6) = 180. However, the angles being added should be supplementary, not adjacent angles. The angles adjacent below the top parallel line and adjacent right to the transversal, labeled (4x - 2) degrees, and the angle adjacent above the lower parallel line and adjacent left to the transversal, labeled (3x + 6) degrees, are corresponding angles, not adjacent angles.
To find the value of x, we should set up an equation using supplementary angles. The sum of the corresponding angles should be equal to 180 degrees. Therefore, the correct equation should be:
4x - 2 + 3x + 6 = 180
Combining like terms, the correct equation becomes:
7x + 4 = 180
Solving for x:
7x = 176
x = 25.1
So the correct value of x is 25.1, which is different from the solution given in B.
To determine which solution for the value of x in the figure is incorrect, we need to assess the given angles.
Let's start by labeling the angles in the figure:
- The angle adjacent below the top parallel line and adjacent right to the transversal is labeled (4x - 2) degrees.
- The angle adjacent above the lower parallel line and adjacent left to the transversal is labeled (3x + 6) degrees.
Now, let's analyze the given options:
A. 4x - 2 = 3x + 6
To solve this equation, we can subtract 3x from both sides: 4x - 3x - 2 = 3x - 3x + 6, resulting in x - 2 = 6. Next, we add 2 to both sides: x - 2 + 2 = 6 + 2, which simplifies to x = 8. This solution seems plausible.
B. 4x - 2 + 3x + 6 = 180
Combining like terms, we get 7x + 4 = 180. To isolate x, we can subtract 4 from both sides: 7x + 4 - 4 = 180 - 4, resulting in 7x = 176. Dividing both sides by 7, we find x = 25.1. However, this solution seems to be incorrect, as it violates the information given in angle A.
By comparing the solutions obtained, we find that option B (x = 25.1) is the one that is incorrect.