Question

1. solve for y.

Explanation:

Step1: Identify angle - relationship

Assume lines \(r\) and \(s\) are parallel and \(q\) is a transversal. The angles \(116^{\circ}\) and \(15y - 4\) are corresponding angles (or alternate - exterior angles if applicable), and for parallel lines, corresponding angles are equal. So we set up the equation \(15y-4 = 116\).

Step2: Solve the equation for \(y\)

Add 4 to both sides of the equation: \(15y-4 + 4=116 + 4\), which simplifies to \(15y=120\).

Step3: Isolate \(y\)

Divide both sides of the equation \(15y = 120\) by 15: \(y=\frac{120}{15}\).

Answer:

\(y = 8\)