Question

in the figure below, l || g. find the values of x and z.

Explanation:

Step1: Use corresponding - angles property

Since \(l\parallel g\), the angle \(x^{\circ}\) and the \(74^{\circ}\) angle are corresponding angles. So \(x = 74\).

Step2: Use linear - pair property

The angle \((4z + 26)^{\circ}\) and \(x^{\circ}\) (which is \(74^{\circ}\)) form a linear - pair. So \((4z + 26)+x=180\). Substitute \(x = 74\) into the equation: \(4z+26 + 74=180\).

Step3: Simplify the equation

Combine like - terms: \(4z+100 = 180\).

Step4: Solve for \(z\)

Subtract 100 from both sides: \(4z=180 - 100=80\). Then divide both sides by 4: \(z=\frac{80}{4}=20\).

Answer:

\(x = 74\), \(z = 20\)