Question

in the figure below, k || l and m || n. find the values of y and x. (5x - 6)° y° 66°

Explanation:

Step1: Use the property of corresponding angles

Since \(k\parallel l\) and \(m\parallel n\), the angle \((5x - 6)^{\circ}\) and the angle adjacent to \(y^{\circ}\) (which is \(180 - y^{\circ}\)) are corresponding angles. Also, \(y^{\circ}\) and \(66^{\circ}\) are supplementary angles (because they are same - side interior angles for parallel lines \(k\) and \(l\) with transversal \(n\)). So \(y+66 = 180\).

Step2: Solve for \(y\)

Subtract 66 from both sides of the equation \(y + 66=180\).
\[y=180 - 66=114\]

Step3: Use the relationship for \(x\)

The angle \((5x - 6)^{\circ}\) and the angle adjacent to \(y^{\circ}\) (which is \(180 - y^{\circ}\)) are equal. Since \(y = 114\), then \(180 - y=180 - 114 = 66\). So \(5x-6=66\).

Step4: Solve for \(x\)

Add 6 to both sides of the equation \(5x-6 = 66\): \(5x=66 + 6=72\). Then divide both sides by 5: \(x=\frac{72}{5}=14.4\)

Answer:

\(y = 114\), \(x = 14.4\)