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:

• $\mathrm{\angle }UWS=6x-18$
• $\mathrm{\angle }QVU={102}^{\circ }$

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 $\boxed{{\displaystyle 20}}$.