In the diagram below, PQ¯¯¯¯¯¯¯¯ ∥ RS¯¯¯¯¯¯¯

Question

. If <UWS = 6x-18 and <QVU = 102, what is the value of x?





(1 point)

Answer 1

To solve for \( x \) in the problem where \( PQ \parallel RS \), we can use the properties of parallel lines and the angles formed by a transversal.

Given the angles:

• \( \angle UWS = 6x - 18 \)
• \( \angle QVU = 102^\circ \)

Since \( PQ \parallel RS \), and \( UWS \) and \( QVU \) are corresponding angles, we can set them equal to each other:

\[ 6x - 18 = 102 \]

Now, we will solve for \( x \).

1. Add 18 to both sides:

\[ 6x = 102 + 18 \] \[ 6x = 120 \]

2. Divide both sides by 6:

\[ x = \frac{120}{6} \] \[ x = 20 \]

Thus, the value of \( x \) is \( \boxed{20} \).