Bot GPT 4-o mini Since PQ is parallel to RS, we can use the properties of angles formed by parallel lines to find the value of \( x \).
From the given information:
- Angle \( UWS = 5x - 12 \)
- Angle \( QVU = 113 \)
Since PQ is parallel to RS and \( UWS \) and \( QVU \) are alternate interior angles, they are equal. Therefore, we can set up the equation:
\[ 5x - 12 = 113 \]
Now we solve for \( x \):
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Add 12 to both sides: \[ 5x = 113 + 12 \] \[ 5x = 125 \]
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Divide by 5: \[ x = \frac{125}{5} = 25 \]
Thus, the value of \( x \) is \( \boxed{25} \).
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