To find the value of \( x \) given that lines PQ and RS are parallel, we can use the properties of angles formed by a transversal cutting across two parallel lines.
Given:
- \( \angle UWS = 5x - 12 \)
- \( \angle QVU = 113^\circ \)
Since lines \( PQ \) and \( RS \) are parallel and \( WV \) acts as a transversal, we can deduce that \( \angle UWS \) and \( \angle QVU \) are corresponding angles. Therefore:
\[ \angle UWS = \angle QVU \]
Substituting the given angles into this equation:
\[ 5x - 12 = 113 \]
Now, we will solve for \( x \):
-
Add \( 12 \) to both sides: \[ 5x = 113 + 12 \] \[ 5x = 125 \]
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Divide both sides by \( 5 \): \[ x = \frac{125}{5} \] \[ x = 25 \]
Thus, the value of \( x \) is \( \boxed{25} \).