Question

two parallel lines are crossed by a transversal. what is the value of x? x = 115 x = 95 x = 65 x = 45

Explanation:

Step1: Use the property of alternate interior angles

When two parallel lines are crossed by a transversal, alternate interior angles are equal.

Step2: Identify the relationship between the given angle and \(x\)

The angle of \(115^{\circ}\) and \(x\) are not alternate - interior angles. But the angle adjacent to \(115^{\circ}\) (let's call it \(y\)) forms a linear pair with \(115^{\circ}\), so \(y = 180 - 115=65^{\circ}\). And \(x\) and \(y\) are alternate interior angles.

Answer:

\(x = 65\)