Question

$\overline { wx } \cong \overline { yz }$, $x$ is the midpoint of $\overline { wy }$.$5x - 5LXB0x =$ type your answer...$xz =$ type your answer...

Explanation:

Step1: Use the mid - point property

Since \(x\) is the mid - point of \(\overline{WY}\), then \(WX = XY\). And given \(\overline{WX}\cong\overline{YZ}\), so \(WX = XY=YZ\). Let \(WX = 5x - 5\), then \(WY=2(5x - 5)\) and \(WZ=WY + YZ=3(5x - 5)\). Also, \(WZ = 6x+30\).
So, \(3(5x - 5)=6x + 30\).

Step2: Expand and solve for \(x\)

Expand the left - hand side: \(15x-15 = 6x + 30\).
Subtract \(6x\) from both sides: \(15x-6x-15=6x - 6x+30\), which gives \(9x-15 = 30\).
Add \(15\) to both sides: \(9x-15 + 15=30 + 15\), so \(9x=45\).
Divide both sides by \(9\): \(x=\frac{45}{9}=5\).

Step3: Find the length of \(WX\)

Substitute \(x = 5\) into \(WX=5x - 5\), then \(WX=5\times5-5=20\).

Step4: Find the length of \(XZ\)

Since \(XZ=XY + YZ\) and \(XY = YZ=WX\), then \(XZ = 20+20=40\).

Answer:

\(x = 5\)
\(XZ=40\)