Question

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

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\) and \(p\parallel q\), the angle \(z\) and the \(115^{\circ}\) angle are corresponding angles. So \(z = 115^{\circ}\).

Step2: Use linear - pair property

The angle \((3y + 2)^{\circ}\) and \(z=115^{\circ}\) form a linear - pair. So \((3y + 2)+115 = 180\).
First, simplify the left - hand side of the equation: \(3y+117 = 180\).
Then, subtract 117 from both sides: \(3y=180 - 117\), \(3y = 63\).
Finally, divide both sides by 3: \(y=\frac{63}{3}=21\).

Answer:

\(z = 115\), \(y = 21\)