Question

if the measure of angle d is 125 degrees, what is the measure of angle e? * 1 point your answer

Explanation:

Step1: Identify angle relationship

Lines \( r \) and \( s \) are parallel, and line \( t \) is a transversal. Angles \( d \) and \( e \) are corresponding angles (or alternate exterior angles, depending on position), but also, since \( d \) and \( e \) should be equal if lines are parallel? Wait, no—wait, actually, if we look at the linear pair or corresponding. Wait, no, let's correct: If angle \( d \) is 125°, and lines \( r \) and \( s \) are parallel, then angle \( e \) and angle \( d \) are corresponding angles? Wait, no, maybe alternate interior? Wait, no, actually, angle \( d \) and angle \( e \): since \( r \parallel s \), and \( t \) is transversal, angle \( e \) should be equal to angle \( d \)? Wait, no, wait—wait, maybe I made a mistake. Wait, no, let's think again. Wait, angle \( d \) and angle \( e \): if \( r \) and \( s \) are parallel, then angle \( e \) is equal to angle \( d \) because they are corresponding angles. Wait, but let's check the diagram: lines \( r \) and \( s \) are parallel, transversal \( t \). So angle \( d \) and angle \( e \) are corresponding angles, so they should be equal. Wait, but 125°? Wait, no, maybe I messed up. Wait, no—wait, maybe angle \( d \) and angle \( e \) are same-side? No, no, the diagram: angle \( d \) is at \( r \) and \( t \), angle \( e \) is at \( s \) and \( t \). So if \( r \parallel s \), then corresponding angles are equal. So angle \( e = \) angle \( d = 125° \)? Wait, but maybe I made a mistake. Wait, no, let's confirm: when two parallel lines are cut by a transversal, corresponding angles are congruent. So angle \( e \) and angle \( d \) are corresponding angles, so they are equal. So angle \( e = 125° \). Wait, but let's check another way: if angle \( d \) is 125°, and angle \( d \) and angle \( a \) are linear pair? No, angle \( d \) and angle \( a \) are adjacent, but angle \( e \) and angle \( d \): since \( r \parallel s \), corresponding angles. So yes, angle \( e = 125° \).

Wait, but maybe I made a mistake. Wait, no, the problem says "if the measure of angle \( d \) is 125 degrees, what is the measure of angle \( e \)". So since \( r \parallel s \), angle \( e \) is equal to angle \( d \) (corresponding angles), so \( e = 125° \).

Step1: Determine angle relationship

Lines \( r \) and \( s \) are parallel, transversal \( t \). Angle \( d \) and angle \( e \) are corresponding angles (by the diagram's position), so they are congruent.

Step2: Calculate angle \( e \)

Since corresponding angles are equal when lines are parallel, \( m\angle e = m\angle d \).

Given \( m\angle d = 125^\circ \), so \( m\angle e = 125^\circ \).

Answer:

\( 125^\circ \)