Question

given: $overleftrightarrow{xz} parallel overleftrightarrow{ac}$ with transversal $overleftrightarrow{ed}$ and expressions representing the angles as marked. determine the value of $x$ and $mangle zyb$. $x = square$ and $mangle zyb=square^{circ}$

Explanation:

Step1: Use corresponding - angles property

Since $\overleftrightarrow{XZ}\parallel\overleftrightarrow{AC}$ and $\overleftrightarrow{ED}$ is a transversal, the corresponding angles are equal. So, $6x = 3x + 9$.

Step2: Solve the equation for $x$

Subtract $3x$ from both sides of the equation $6x=3x + 9$. We get $6x-3x=3x + 9-3x$, which simplifies to $3x=9$. Then divide both sides by 3: $x=\frac{9}{3}=3$.

Step3: Find the measure of $\angle ZYB$

Substitute $x = 3$ into the expression for $\angle ZYB$ which is $6x$. So, $m\angle ZYB=6\times3 = 18$.

Answer:

$x = 3$ and $m\angle ZYB=18$