Question

9 given that lines a, b, and c are parallel lines, find the value of x, y, and x + y

Explanation:

Step1: Find the value of \(x\)

When two parallel lines are cut by a transversal, corresponding angles are equal. So \(x = 96^{\circ}\) (corresponding angles).

Step2: Find the value of \(y\)

When two parallel lines are cut by a transversal, alternate - interior angles are equal. The angle adjacent to \(y\) is \(96^{\circ}\) (vertical angles). Since \(y\) and the \(96^{\circ}\) angle are supplementary (linear pair), \(y=180 - 96=84^{\circ}\)

Step3: Find the value of \(x + y\)

Substitute \(x = 96\) and \(y = 84\) into \(x + y\). Then \(x + y=96+84 = 180^{\circ}\)

Answer:

1. \(x = 96\) (Option b)
2. \(x + y=180\) (Option c)
3. \(y = 84\) (Option a)