To find the value of \( x \), we can use the fact that corresponding angles are congruent when parallel lines are cut by a transversal. Since RS is parallel to PQ, the angles \( \angle PVU \) and \( \angle TWS \) are likely corresponding angles.
Given:
\[ \angle PVU = 4x - 7 \] \[ \angle TWS = 2x + 27 \]
Since \( \angle PVU \) and \( \angle TWS \) are equal, we can set up the equation:
\[ 4x - 7 = 2x + 27 \]
Now, let's solve for \( x \):
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Subtract \( 2x \) from both sides: \[ 4x - 2x - 7 = 27 \] This simplifies to: \[ 2x - 7 = 27 \]
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Add 7 to both sides: \[ 2x = 27 + 7 \] Simplifying gives: \[ 2x = 34 \]
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Divide by 2: \[ x = \frac{34}{2} = 17 \]
Thus, the value of \( x \) is \( \boxed{17} \).
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