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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.
The incorrect solution is A. 4x - 2 = 3x + 6. This is incorrect because when solving this equation, we get x = 8. However, in the given figure, the correct value for x should be 25. Therefore, the solution A is incorrect.
The incorrect solution for the value of x is B.
In solution B, it states that "4x – 2 + 3x + 6 = 180." However, this equation is incorrect because it combines the angles on the left and right sides of the transversal.
The correct equation should have been "4x – 2 + (3x +6) = 180." This equation shows that the sum of the two adjacent angles on the same side of the transversal should equal 180 degrees.
By solving the correct equation, we would get:
4x – 2 + 3x + 6 = 180
7x + 4 = 180
7x = 180 - 4
7x = 176
x = 176 / 7
x = 25
Therefore, the correct value of x is 25, not 8.