Given that lines AB and CD are parallel, we can use the properties of corresponding angles and alternate interior angles to solve the problem.
You have mentioned that there are two types of angles: (3x - 35)° and 128°. If these angles are corresponding or alternate interior angles, we can set up the equation:
\[ 3x - 35 = 128 \]
Now, let's solve for \( x \):
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Add 35 to both sides: \[ 3x - 35 + 35 = 128 + 35 \] \[ 3x = 163 \]
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Divide both sides by 3: \[ x = \frac{163}{3} \]
This calculation gives us:
\[ x \approx 54.33 \]
This value does not correspond to any of the options provided (232, 19, 128, 29).
Let's check the other scenario in which \( 6 \) measures of \( (3x - 35)° \) account for supplementary angles with the \( 8 \) measures of \( 128° \). If those angles together sum to \( 180° \):
\[ 6(3x - 35) + 8 \cdot 128 = 180 \]
Calculating:
- \( 8 \cdot 128 = 1024 \).
Now substitute this value back into the equation:
\[ 6(3x - 35) + 1024 = 180 \]
Rearranging gives:
\[ 6(3x - 35) = 180 - 1024 \] \[ 6(3x - 35) = -844 \]
Now, divide both sides by 6:
\[ 3x - 35 = -\frac{844}{6} \] \[ 3x - 35 = -140.67 \]
Adding 35 to both sides:
\[ 3x = -140.67 + 35 \] \[ 3x = -105.67 \]
Dividing again by 3 gives no rational solution here, suggesting a discrepancy in the given measurements.
To confirm the correct approach, simply returning to the corresponding angles with:
- If \( (3x - 35) + 128 = 180 \):
Set up:
\[ 3x - 35 + 128 = 180 \] \[ 3x + 93 = 180 \] \[ 3x = 87 \] \[ x = 29 \]
Thus the solution aligns with option D. The value of \( x \) is indeed:
\[ \boxed{29} \]
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