Question

in the figure shown, lines m and n are parallel, and line t intersects both lines. if x > 125, which of the following must be true? note: figure not drawn to scale. y > 55 x + y > 180 y < 55 x + y < 180

Explanation:

Step1: Recall angle - relationship

Since lines \(m\) and \(n\) are parallel and \(t\) is a transversal, \(x\) and \(y\) are supplementary angles, so \(x + y=180^{\circ}\).

Step2: Given \(x>125\)

If \(x + y = 180\), then \(y=180 - x\).

Step3: Substitute the inequality

Since \(x>125\), then \(y = 180 - x<180 - 125\).

Step4: Calculate the value of \(y\)

\(180-125 = 55\), so \(y<55\).

Answer:

\(y < 55\)