Question

given that the quadrilateral wxyz is a parallelogram,
\\( \overline { w x } = 10 x + 36 \\) and \\( \overline { y z } = 9 x + 42 \\), what is \\( \overline { w x } \\)?
\\( \overline { w x } = \\)

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So, $\overline{WX}=\overline{YZ}$.
$$10x + 36=9x + 42$$

Step2: Solve the equation for \(x\)

Subtract \(9x\) from both sides:
$$10x-9x+36=9x - 9x+42$$
$$x+36=42$$
Subtract \(36\) from both sides:
$$x+36 - 36=42 - 36$$
$$x = 6$$

Step3: Find the length of \(\overline{WX}\)

Substitute \(x = 6\) into the expression for \(\overline{WX}\) (\(\overline{WX}=10x + 36\)):
$$\overline{WX}=10\times6+36$$
$$\overline{WX}=60 + 36$$
$$\overline{WX}=96$$

Answer:

\(96\)