To solve for \(x\) and \(y\) given the relationships between the angles, we need to use the fact that angles formed by a transversal crossing parallel lines have specific relationships (such as corresponding angles being equal or alternate interior angles being equal).
From your question, we have:
\[ B = 3x + 16 \] \[ G = 2x + 29 \] \[ A = 2y + 17 \]
Since lines \(x\) and \(y\) are parallel, we assume that angle \(B\) and angle \(G\) are equal (corresponding angles). Thus, we set the equations for \(B\) and \(G\) equal to each other:
\[ 3x + 16 = 2x + 29 \]
Now, solve for \(x\):
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Subtract \(2x\) from both sides: \[ 3x - 2x + 16 = 29 \] This simplifies to: \[ x + 16 = 29 \]
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Subtract \(16\) from both sides: \[ x = 29 - 16 \] Thus, \[ x = 13 \]
Next, if we want to find \(y\), we need more information about the angles related to \(A\). Since angle \(A\) is at line \(y\), we assume angle \(A\) is equal to one of the angles related to \(B\) or \(G\) (for example, angle \(B\) because \(A\) and \(B\) are alternate interior angles).
Assuming \(A = B\):
\[ 2y + 17 = 3x + 16 \]
Now we substitute \(x\) with \(13\):
\[ 2y + 17 = 3(13) + 16 \]
This simplifies to:
\[ 2y + 17 = 39 + 16 \] \[ 2y + 17 = 55 \]
Now, solve for \(y\):
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Subtract \(17\) from both sides: \[ 2y = 55 - 17 \] This simplifies to: \[ 2y = 38 \]
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Divide by \(2\): \[ y = \frac{38}{2} \] Thus, \[ y = 19 \]
So, the final values are:
\[ x = 13 \] \[ y = 19 \]
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