Question

given the diagram, line s is a transversal. what value of y proves g||h? y =

Explanation:

Step1: Identify corresponding angles

If \(g\parallel h\), then the \(48^{\circ}\) angle and \((x + y)^{\circ}\) are corresponding angles and are equal. So \(x + y=48\). Also, \((x + y)^{\circ}\) and \((3x)^{\circ}\) are supplementary (linear - pair), so \(x + y+3x = 180\).

Step2: Substitute \(x + y = 48\) into the second - equation

Substituting \(x + y = 48\) into \(x + y+3x = 180\), we get \(48+3x = 180\).
Solve for \(x\):
\[

$$\begin{align*} 3x&=180 - 48\\ 3x&=132\\ x& = 44 \end{align*}$$

\]

Step3: Find the value of \(y\)

Since \(x + y=48\) and \(x = 44\), then \(y=48 - x\).
Substitute \(x = 44\) into \(y = 48 - x\), we get \(y=48-44 = 4\).

Answer:

\(4\)