Question

a pair of parallel lines is cut by a transversal, as shown in the figure: which of the following best represents the relationship between angles x and y? x = y x = 180 degrees - y y = 180 degrees - x x = 2y

Explanation:

Step1: Use the property of parallel lines and transversal

When a pair of parallel lines is cut by a transversal, \(x\) and \(y\) are alternate - interior angles. But wait, no! Wait, \(x\) and the angle adjacent to \(y\) (on the same side of the transversal) are supplementary. Wait, no, actually, \(x\) and \(y\) are related as \(x + y=180^{\circ}\) (co - interior angles). But wait, no, wait the first line: \(x\) is an angle, and the angle adjacent to \(x\) (linear pair) is equal to \(y\) (alternate interior angles). Since \(x\) and its adjacent angle form a linear pair (\(x+\text{adjacent angle}=180^{\circ}\)), and \(\text{adjacent angle}=y\) (alternate interior angles for parallel lines cut by a transversal).
So \(x + y=180^{\circ}\), which can be rewritten as \(x = 180^{\circ}-y\)

Answer:

\(x = 180\) degrees \(-y\)