Question

given that the quadrilateral wxyz is a parallelogram,
\\( \overline { w x } = 22 x + 9 \\) and \\( \overline { y z } = 16 x + 33 \\), what is \\( \overline { w x } \\)?
\\( \overline { w x } = \\)

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So, $\overline{WX}=\overline{YZ}$.
$$22x + 9=16x + 33$$

Step2: Solve the equation for \(x\)

Subtract \(16x\) from both sides:
$$22x-16x + 9=16x-16x + 33$$
$$6x+9 = 33$$
Subtract \(9\) from both sides:
$$6x+9 - 9=33 - 9$$
$$6x=24$$
Divide both sides by \(6\):
$$x=\frac{24}{6}=4$$

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

Substitute \(x = 4\) into the expression for \(\overline{WX}\) (\(\overline{WX}=22x + 9\)):
$$\overline{WX}=22\times4+9$$
$$=88 + 9$$
$$=97$$

Answer:

\(97\)