Question

two parallel lines are crossed by a transversal. what is the value of d? 125° d° q r s d = 55 d = 75 d = 125 d = 155

Explanation:

Step1: Identify Angle Relationship

The 125° angle and \( d^\circ \) are vertical angles? No, wait—wait, the two lines are parallel, and the transversal creates a linear pair? Wait, no, actually, the 125° and \( d \) are... Wait, no, looking at the diagram, the 125° and \( d \) are adjacent? Wait, no, when two parallel lines are cut by a transversal, consecutive interior angles? Wait, no, actually, the 125° and \( d \) are supplementary? Wait, no, wait—wait, the angle of 125° and \( d \) are vertical angles? No, wait, no. Wait, the two parallel lines (r and s) are cut by transversal q. The angle of 125° and \( d \) are... Wait, no, actually, the 125° and \( d \) are same-side? Wait, no, wait, the 125° and \( d \) are adjacent? Wait, no, let's think again. Wait, the 125° angle and \( d \) are supplementary? Wait, no, 180 - 125 = 55? No, that's not. Wait, no, wait, the 125° and \( d \) are equal? Wait, no, wait, the diagram: the two parallel lines (r and s) are cut by transversal q. The angle of 125° and \( d \) are vertical angles? No, wait, no. Wait, the 125° angle and \( d \) are same-side interior? No, wait, no. Wait, maybe the 125° and \( d \) are equal. Wait, no, 125 and d: if the lines are parallel, then corresponding angles are equal. Wait, the 125° angle and \( d \) are equal? Wait, no, 125 + d = 180? No, 180 - 125 = 55, but that's not an option. Wait, no, wait, the options are 55, 75, 125, 155. Wait, maybe the 125° and \( d \) are vertical angles? Wait, no, vertical angles are equal. Wait, no, the 125° and \( d \) are adjacent? Wait, no, let's look at the diagram again. The two parallel lines (r and s) are cut by transversal q. The angle of 125° is above line s, and \( d \) is below? Wait, no, the diagram shows the transversal crossing the two parallel lines (r and s, which are vertical). The transversal is q, which is a slant line. The angle of 125° is between the transversal and line s (upper part), and \( d \) is between transversal and line s (lower part). Wait, so 125° and \( d \) are supplementary? 180 - 125 = 55? No, that's not. Wait, no, wait, maybe the 125° and \( d \) are equal. Wait, no, 125 is an option. Wait, the options include d=125. Wait, maybe the 125° and \( d \) are vertical angles? No, vertical angles are equal. Wait, no, maybe the 125° and \( d \) are corresponding angles. Wait, the two parallel lines (r and s) are cut by transversal q. The angle of 125° on line r and \( d \) on line s: if they are corresponding angles, then they are equal. Wait, but in the diagram, the 125° is on line s? Wait, no, the diagram: the two parallel lines (r and s) are vertical, with arrows up and down. The transversal q is a slant line from bottom left to top right. The angle of 125° is between transversal q and line s (upper part), and \( d \) is between transversal q and line s (lower part). Wait, so 125° and \( d \) are supplementary? 180 - 125 = 55? No, that's not. Wait, no, wait, maybe the 125° and \( d \) are equal. Wait, no, 125 is an option. Wait, maybe the 125° and \( d \) are vertical angles. Wait, vertical angles are equal. So if the 125° angle and \( d \) are vertical angles, then d=125. Wait, that makes sense. Wait, the 125° angle and \( d \) are vertical angles, so they are equal. So d=125.

Step2: Confirm the Relationship

Since the two angles (125° and \( d \)) are vertical angles (formed by the intersection of the transversal and the parallel line s), vertical angles are equal. So \( d = 125 \).

Answer:

d = 125 (Option: \( d = 125 \))