Question

in the figure below, h || n. find the values of x and y.

Explanation:

Step1: Use corresponding - angles property

Since \(h\parallel n\), the angle \(x^{\circ}\) and the \(76^{\circ}\) angle are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So \(x = 76\).

Step2: Use vertical - angles property

The angle \((4y - 20)^{\circ}\) and the \(76^{\circ}\) angle are vertical angles. Vertical angles are equal. So we set up the equation \(4y-20=76\).
Add 20 to both sides of the equation: \(4y-20 + 20=76 + 20\), which simplifies to \(4y=96\).
Divide both sides by 4: \(y=\frac{96}{4}=24\).

Answer:

\(x = 76\), \(y = 24\)