Question

in the figure below, m || h. find the values of z and x.

Explanation:

Step1: Use the property of parallel lines (alternate - interior angles)

Since \(m\parallel n\), then \(4x - 76=60\) (alternate - interior angles are equal).
Solve the equation \(4x-76 = 60\) for \(x\):
Add \(76\) to both sides: \(4x=60 + 76\), so \(4x=136\).
Divide both sides by \(4\): \(x=\frac{136}{4}=34\).

Step2: Use the property of supplementary angles

\(z\) and \(60^{\circ}\) are supplementary angles (because \(m\parallel n\) and they form a linear - pair - like relationship for the transversal). So \(z+60 = 180\).
Subtract \(60\) from both sides: \(z=180 - 60=120\).

Answer:

\(x = 34\), \(z = 120\)