Question

$\overline{yz} \parallel \overline{vx}$. find $wy$.

Explanation:

Step1: Identify segment lengths

Given $WV = 8$, $WZ = 24$, so $VZ = WZ - WV = 24 - 8 = 16$. Let $WX = x$, so $WY = x + 34$.

Step2: Apply Triangle Proportionality Theorem

Since $\overline{YZ} \parallel \overline{VX}$, $\frac{WX}{XY} = \frac{WV}{VZ}$
Substitute values: $\frac{x}{34} = \frac{8}{16}$

Step3: Solve for $x$

Simplify $\frac{8}{16} = \frac{1}{2}$, so $\frac{x}{34} = \frac{1}{2}$
$x = 34 \times \frac{1}{2} = 17$

Step4: Calculate $WY$

$WY = x + 34 = 17 + 34$

Answer:

51