Question

in the figure below, (hparallel l) and (jparallel k). find the values of (y) and (x).

Explanation:

Step1: Use corresponding - angles property

Since \(h\parallel l\) and \(j\parallel k\), the angle \(y^{\circ}\) and the \(85^{\circ}\) angle are corresponding angles. So \(y = 85\).

Step2: Use alternate - exterior angles property

The angle \((4x - 11)^{\circ}\) and the \(85^{\circ}\) angle are alternate - exterior angles. So we set up the equation \(4x-11=85\).

Step3: Solve the equation for \(x\)

Add 11 to both sides of the equation \(4x - 11=85\): \(4x=85 + 11\), so \(4x=96\). Then divide both sides by 4: \(x=\frac{96}{4}=24\).

Answer:

\(y = 85\), \(x = 24\)