Question

1. in the diagram below, transversal $overline{tu}$ intersects $overline{pq}$ and $overline{rs}$ at $v$ and $w$, respectively. if $mangle tvq=(5x - 22)^{circ}$ and $mangle vws=(3x + 10)^{circ}$, for which value of $x$ is $overline{pq}$ parallel to $overline{rs}$?

Explanation:

Step1: Recall parallel - line property

When $\overline{PQ}\parallel\overline{RS}$, $\angle TVQ$ and $\angle VWS$ are corresponding angles and are equal. So we set up the equation $5x - 22=3x + 10$.

Step2: Solve the equation for $x$

Subtract $3x$ from both sides: $5x-3x - 22=3x-3x + 10$, which simplifies to $2x-22 = 10$.

Step3: Isolate the term with $x$

Add 22 to both sides: $2x-22 + 22=10 + 22$, getting $2x=32$.

Step4: Find the value of $x$

Divide both sides by 2: $\frac{2x}{2}=\frac{32}{2}$, so $x = 16$.

Answer:

$x = 16$