In the diagram below, PQ∥RS

Question

. If ∠UWS = 4x−18
and ∠QVU = 102°
, what is the value of x?

(1 point)
x=

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Answer 1

To find the value of \( x \), we will use the fact that \( PQ \parallel RS \). This gives us the relationship between certain angles due to the properties of parallel lines and transversals.

Given the angles:

• \( \angle UWS = 4x - 18 \)
• \( \angle QVU = 102° \)

Since \( PQ \parallel RS \), the angles \( \angle UWS \) and \( \angle QVU \) are corresponding angles. Therefore, they are equal:

\[ 4x - 18 = 102 \]

Now, solve for \( x \):

1. Add \( 18 \) to both sides: \[ 4x = 102 + 18 \] \[ 4x = 120 \]

2. Divide both sides by \( 4 \): \[ x = \frac{120}{4} \] \[ x = 30 \]

Thus, the value of \( x \) is \( \boxed{30} \).