Given that lines \( x \) and \( y \) are parallel, it means that the angles formed by the transversal that intersects these lines are congruent.
Since you didn't specify how angles \( A \), \( B \), and \( G \) are positioned in relation to \( x \) and \( y \), a common assumption would be to assume that angles \( B \) and \( G \) are corresponding or alternate interior angles. We will set up an equation based on this assumption.
Assuming angles \( B \) and \( G \) are corresponding (or alternate interior angles), we can set them equal to each other:
\[ B = G \]
Substituting the expressions for \( B \) and \( G \) into the equation gives:
\[ 3x + 16 = 2x + 29 \]
Now, let's solve for \( x \):
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Subtract \( 2x \) from both sides: \[ 3x - 2x + 16 = 29 \] \[ x + 16 = 29 \]
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Subtract \( 16 \) from both sides: \[ x = 29 - 16 \] \[ x = 13 \]
Now, let's verify if we need to involve angle \( A \), which is expressed as \( A = 2y + 17 \). However, since angle \( A \) is related to another line \( y \) and we already established the relationship between \( B \) and \( G \) is sufficient for determining \( x \), we will stick with \( x = 13 \).
Thus, the value of \( x \) is:
\[ \boxed{13} \]