Question

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

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\) and \(p\) is a transversal, \(y = 74^{\circ}\) (corresponding angles are equal).

Step2: Use alternate - interior angles property

Since \(p\parallel q\) and \(m\) is a transversal, the angle \((4x - 6)^{\circ}\) and \(y^{\circ}\) are alternate - interior angles. So \(4x-6=y\).
Substitute \(y = 74\) into the equation \(4x-6=y\). We get \(4x-6 = 74\).
Add 6 to both sides of the equation: \(4x=74 + 6\), so \(4x=80\).
Divide both sides by 4: \(x=\frac{80}{4}=20\).

Answer:

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