Question

1. parallel lines m and n intersect parallel lines x and y, representing two sets of intersecting railroad tracks. at what angles do the tracks intersect? 125° m n x y

Explanation:

Step1: Recall angle - relationships in parallel lines

When two parallel lines are intersected by a transversal, corresponding angles are equal, alternate - interior angles are equal, and consecutive interior angles are supplementary. Here, the given angle of \(125^{\circ}\) and the angle of intersection of the tracks are either corresponding or alternate - interior angles.

Step2: Determine the angles of intersection

Since the angles formed by the intersection of the two sets of parallel lines (the tracks) are either corresponding or alternate - interior to the given \(125^{\circ}\) angle, the angles of intersection are \(125^{\circ}\) and its supplementary angle. The supplementary angle of \(125^{\circ}\) is \(180 - 125=55^{\circ}\).

Answer:

The tracks intersect at angles of \(55^{\circ}\) and \(125^{\circ}\)