Question

in the figure below, k || l and m || n. find the values of z and x.

Explanation:

Step1: Use corresponding - angles property

Since \(k\parallel l\) and \(m\) is a transversal, the angle of \(77^{\circ}\) and the angle \((6x - 73)^{\circ}\) are corresponding angles. So, \(6x-73 = 77\).

Step2: Solve the equation for \(x\)

Add 73 to both sides of the equation \(6x-73 = 77\):
\[6x=77 + 73\]
\[6x=150\]
Divide both sides by 6: \(x=\frac{150}{6}=25\).

Step3: Use vertical - angles property

Since \(z^{\circ}\) and the angle of \(77^{\circ}\) are vertical angles, \(z = 77\).

Answer:

\(x = 25\), \(z = 77\)