Question

1. lines l and m are parallel and intersect transversal p, as shown in the diagram below. write and solve an equation to solve for the value of n.

Explanation:

Step1: Use corresponding - angles property

Since lines \(l\) and \(m\) are parallel and \(p\) is a transversal, the corresponding angles are equal. So, \(3n + 16=5n + 4\).

Step2: Isolate the variable terms

Subtract \(3n\) from both sides of the equation: \(3n+16 - 3n=5n + 4-3n\), which simplifies to \(16 = 2n+4\).

Step3: Isolate the term with \(n\)

Subtract 4 from both sides: \(16 - 4=2n+4 - 4\), resulting in \(12 = 2n\).

Step4: Solve for \(n\)

Divide both sides by 2: \(\frac{12}{2}=\frac{2n}{2}\), so \(n = 6\).

Answer:

\(n = 6\)