Question

in the figure below, m || n and p || q. find the values of x and z.

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\) and \(p\parallel q\), the angle \(x^{\circ}\) and the \(69^{\circ}\) angle are corresponding angles. So \(x = 69\).

Step2: Use vertical - angles property

The angle \((6z - 69)^{\circ}\) and the \(69^{\circ}\) angle are vertical angles. So we set up the equation \(6z-69 = 69\).

Step3: Solve the equation for \(z\)

Add 69 to both sides of the equation \(6z-69 = 69\): \(6z=69 + 69\), so \(6z=138\). Then divide both sides by 6: \(z=\frac{138}{6}=23\).

Answer:

\(x = 69\), \(z = 23\)