Question

1. relationship: ______ b= ______ (diagram shows intersecting lines with a 53° angle and angle ( b ) in a geometric figure with triangles)

Explanation:

Step1: Identify angle relationship

The angle \( b \) and the \( 53^\circ \) angle are vertical angles? No, wait, they are adjacent supplementary? Wait, no, actually, they are vertical angles? Wait, no, looking at the diagram, the two angles ( \( b \) and \( 53^\circ \)) are vertical angles? Wait, no, maybe they are supplementary? Wait, no, actually, in the diagram, the two angles form a linear pair? Wait, no, the angle \( b \) and the \( 53^\circ \) angle are vertical angles? Wait, no, let's think again. Wait, the two angles are vertical angles? No, vertical angles are equal. Wait, no, maybe they are supplementary? Wait, no, the diagram shows that \( b \) and \( 53^\circ \) are vertical angles? Wait, no, maybe I made a mistake. Wait, actually, the angle \( b \) and the \( 53^\circ \) angle are vertical angles? No, vertical angles are opposite each other when two lines intersect. Wait, in the diagram, the two lines intersect, so \( b \) and \( 53^\circ \) are vertical angles? Wait, no, vertical angles are equal. Wait, no, maybe they are supplementary? Wait, no, the sum of a linear pair is \( 180^\circ \). Wait, maybe the angle \( b \) and \( 53^\circ \) are vertical angles? Wait, no, let's check again. Wait, the diagram: two triangles, with a transversal? Wait, no, the two angles \( b \) and \( 53^\circ \) are vertical angles? Wait, no, vertical angles are equal. Wait, maybe the angle \( b \) is equal to \( 53^\circ \)? Wait, no, that can't be. Wait, maybe they are supplementary? Wait, no, the sum of \( b \) and \( 53^\circ \) is \( 180^\circ \)? Wait, no, that would be a linear pair. Wait, maybe the angle \( b \) is equal to \( 53^\circ \) because they are vertical angles. Wait, let's confirm: when two lines intersect, vertical angles are equal. So if the two angles are vertical angles, then \( b = 53^\circ \). Wait, but maybe I'm wrong. Wait, the diagram: the angle \( 53^\circ \) and angle \( b \) are opposite each other when two lines cross, so they are vertical angles. Therefore, \( b = 53^\circ \).

Step2: Calculate \( b \)

Since \( b \) and \( 53^\circ \) are vertical angles, they are equal. So \( b = 53^\circ \).

Answer:

\( b = 53^\circ \) (Relationship: Vertical angles are equal)