Question

two parallel lines are intersected by a third line so that angles 1 and 5 are congruent. which statement is true about angles 3 and 5? they are acute. they are congruent. they are complementary. they are supplementary.

Explanation:

Step1: Recall the property of adjacent angles

Angles \(1\) and \(3\) are adjacent and form a linear pair. So, \(\angle1+\angle3 = 180^{\circ}\) (by the linear - pair postulate: adjacent angles formed by two intersecting lines are supplementary)

Step2: Use the given congruent angles

Given \(\angle1\cong\angle5\) (i.e., \(\angle1=\angle5\))

Step3: Substitute \(\angle1\) with \(\angle5\)

Substitute \(\angle1\) in \(\angle1+\angle3 = 180^{\circ}\) with \(\angle5\). We get \(\angle5+\angle3=180^{\circ}\)

If the sum of two angles is \(180^{\circ}\), the angles are supplementary. So, angles \(3\) and \(5\) are supplementary.

Answer:

They are supplementary