Which solution for the value of x in the figure below is incorrect? Explain.
GEOA_03_L10_Q17
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 B. 4x – 2 + 3x + 6 = 180.
To find the measure of angles using parallel lines and a transversal, we set up equations using angle relationships. In this case, the angles adjacent to the parallel lines are corresponding angles, which means they are congruent.
The given angles are labeled (4x – 2) degrees and (3x + 6) degrees.
If we set up the equation for the corresponding angles, it should be (4x – 2) = (3x + 6).
Solving this equation, we get x = 8.
However, in solution B, the equation (4x – 2) + (3x + 6) = 180 is incorrectly set up. This equation suggests that the sum of the two angles should be 180 degrees, which is not the case for corresponding angles. So, the solution x = 25.1 obtained from this equation is incorrect.
To determine which solution for the value of x is incorrect, we can analyze the given angles and their relationships.
The angle adjacent below the top parallel line and adjacent right to the transversal is labeled as (4x - 2) degrees.
The angle adjacent above the lower parallel line and adjacent left to the transversal is labeled as (3x + 6) degrees.
To find the value of x, we need to set up an equation involving these angles.
A. 4x - 2 = 3x + 6
This equation represents the fact that the two adjacent angles are equal. To solve for x, we can subtract 3x from both sides of the equation:
4x - 3x - 2 = 6
x - 2 = 6
Then, we add 2 to both sides:
x = 8
So, option A indicates that the value of x is 8.
B. 4x - 2 + 3x + 6 = 180
This equation is based on the fact that the sum of the interior angles on the same side of the transversal is equal to 180 degrees. To solve for x, we combine like terms:
7x + 4 = 180
Then, we subtract 4 from both sides:
7x = 176
Finally, we divide both sides by 7:
x = 25.1
So, option B indicates that the value of x is 25.1.
Comparing the calculated values of x with the options given:
A. x = 8 (Correct)
B. x = 25.1 (Correct)
Therefore, both options A and B are correct, and there is no incorrect solution provided.