Question

1. in the diagram below, lines n and m are cut by transversals p and q. what value of x would make lines n and m parallel?

Explanation:

Step1: Identify angle - related property

When two parallel lines are cut by a transversal, corresponding angles are equal.

Step2: Set up equation

We know that the angle corresponding to the sum of \(x\) and \(30^{\circ}\) is \(80^{\circ}\). So \(x + 30^{\circ}=80^{\circ}\).

Step3: Solve for \(x\)

Subtract \(30^{\circ}\) from both sides of the equation: \(x=80^{\circ}- 30^{\circ}\).

Answer:

\(x = 50^{\circ}\)