Question

9.
(3n - 47)°
(n + 7)°
m∠abc = 118

Explanation:

Step1: Identify Angle Relationship

Since lines \(AB\) and \(CD\) are parallel (indicated by arrow marks) and the transversal creates same - side interior angles, the sum of \((3n - 47)^{\circ}\) and \((n + 7)^{\circ}\) is \(180^{\circ}\)? Wait, no, looking at the diagram, actually \(\angle ABC\) and the angle \((n + 7)^{\circ}\) are same - side interior angles? Wait, no, the given angle \(\angle ABC=(3n - 47)^{\circ}\) and we know that \(m\angle ABC = 118^{\circ}\), so we can set up the equation \(3n-47 = 118\) to solve for \(n\), or maybe the two angles \((3n - 47)^{\circ}\) and \((n + 7)^{\circ}\) are supplementary? Wait, let's re - examine.

Wait, the problem might be to solve for \(n\) given that \(m\angle ABC=(3n - 47)^{\circ}=118^{\circ}\). Let's do that.

Step2: Solve for \(n\)

We have the equation \(3n-47 = 118\).
First, add 47 to both sides of the equation:
\(3n-47 + 47=118 + 47\)
\(3n=165\)
Then, divide both sides by 3:
\(n=\frac{165}{3}=55\)

Wait, but maybe the two angles \((3n - 47)^{\circ}\) and \((n + 7)^{\circ}\) are supplementary. Let's check. If \(3n-47 + n + 7=180\), then \(4n-40 = 180\), \(4n=220\), \(n = 55\). Then \((n + 7)^{\circ}=(55 + 7)^{\circ}=62^{\circ}\), and \(118^{\circ}+62^{\circ}=180^{\circ}\), which makes sense for same - side interior angles. So the value of \(n\) is 55.

Answer:

\(n = 55\)