In the diagram, PQ is parallel to RS.

Question

If angle UWS = 5x - 12 and angle QVU = 113, what is the value of x?

20
25
67
113

Answer 1

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 \( x \):

1. Add 12 to both sides: \[ 5x = 113 + 12 \] \[ 5x = 125 \]

2. Divide by 5: \[ x = \frac{125}{5} = 25 \]

Thus, the value of \( x \) is \( \boxed{25} \).