Question

1. solve for y

Explanation:

Step1: Use the property of same - side interior angles

When two parallel lines \(r\) and \(s\) are cut by a transversal \(q\), the sum of same - side interior angles is \(180^{\circ}\). So, \(116+(15y - 4)=180\).

Step2: Simplify the equation

First, simplify the left - hand side of the equation: \(116 + 15y-4=180\), which becomes \(15y+112 = 180\).
Then, subtract \(112\) from both sides: \(15y=180 - 112\), so \(15y=68\).

Step3: Solve for \(y\)

Divide both sides of the equation \(15y = 68\) by \(15\): \(y=\frac{68}{15}\approx4.53\).

Answer:

\(4.53\)