Question

1. two parallel lines, $overline{rq}$ and $overline{xy}$ are intersected by a third line, transversal $overline{pu}$, as shown below. if $mangle psq = 92^{circ}$ and $mangle sty=(8x - 28)^{circ}$, find the value of $x$ algebraically.

Explanation:

Step1: Identify angle - relationship

Since $\overline{RQ}\parallel\overline{XY}$ and $\overline{PU}$ is a transversal, $\angle PSQ$ and $\angle STY$ are corresponding angles, so $\angle PSQ=\angle STY$.

Step2: Set up equation

We know that $m\angle PSQ = 92^{\circ}$ and $m\angle STY=(8x - 28)^{\circ}$, so we set up the equation $8x-28 = 92$.

Step3: Solve the equation

Add 28 to both sides: $8x-28 + 28=92 + 28$, which simplifies to $8x=120$. Then divide both sides by 8: $x=\frac{120}{8}=15$.

Answer:

$x = 15$