In a parallelogram, opposite angles are equal and adjacent angles are supplementary, meaning they add up to 180 degrees.
Given:
- Angle B = \(4x - 18\)
- Angle D = \(2x + 42\)
Since B and D are adjacent angles in the parallelogram, we can set up the equation:
\[ (4x - 18) + (2x + 42) = 180 \]
Now, combine like terms:
\[ 4x + 2x - 18 + 42 = 180 \] \[ 6x + 24 = 180 \]
Next, subtract 24 from both sides:
\[ 6x = 156 \]
Now, divide by 6:
\[ x = 26 \]
However, none of the given options contain this value. Let’s double-check the calculation.
The angles should also satisfy the condition of a parallelogram where opposite angles are equal. Thus Angle A = Angle C and:
Using the fact: \[ B + D = 180^\circ \] \[ (4x - 18) + (2x + 42) = 180 \] Which simplifies correctly to: \[ 6x + 24 = 180 \rightarrow 6x = 156 \rightarrow x = 26 \]
Since the calculation holds true, and no options match, it appears there is a mistake with provided options or there may have been a misunderstanding in interpretation.
But if we check the sum of angles based on the provided options, only option b was closest at 20 but contradicts with actual calculation. Thus confidently the value of x indicates as \( x = 26 \) based on mathematical operations and parallelogram properties.
Final value of x from above calculation is 26, suggesting rechecking question if mistaken or forgotten supplementary conditions/angles.