Question

structure in the diagram, $jklm \sim efgh$. find the values of $x$, $y$, and $z$.
$x=\square,y=\square,z=\square$

Explanation:

Step1: Find similarity ratio

$\text{Ratio} = \frac{JK}{FG} = \frac{20}{11}$

Step2: Solve for $x$

Set up proportion: $\frac{x}{8} = \frac{20}{11}$
$x = 8 \times \frac{20}{11} = \frac{160}{11}$

Step3: Solve for $y$

Set up proportion: $\frac{y}{30} = \frac{11}{20}$
$y = 30 \times \frac{11}{20} = \frac{330}{20} = 30$

Step4: Solve for $z$

Corresponding angles are equal: $z = \angle J = 65^\circ$

Answer:

$x= \frac{160}{11}$, $y= \frac{330}{11}=30$, $z=65$