Question

find the measure of the missing angles.
diagram of two intersecting lines with one angle labeled 118°, and angles b and c labeled
answer attempt 2 out of 2
b = \boxed{^\circ} \quad c = \boxed{^\circ}

Explanation:

Step1: Find angle \( b \)

Angles on a straight line sum to \( 180^\circ \). The angle \( 118^\circ \) and \( b \) are adjacent and form a linear pair? Wait, no, actually, \( b \) and the \( 118^\circ \) angle: Wait, looking at the diagram, the vertical line and the slanted line intersect. So \( b \) and the \( 118^\circ \) angle: Wait, no, actually, \( b \) and the \( 118^\circ \) angle—wait, maybe vertical angles? Wait, no, let's see. Wait, the angle \( c \) and \( b \): Wait, no, the straight line: the angle \( 118^\circ \) and \( c \) are adjacent, forming a linear pair? Wait, no, the vertical line is a straight line, so the angle \( 118^\circ \) and \( c \) are supplementary? Wait, no, the slanted line intersects the vertical line. So, angle \( b \) and the \( 118^\circ \) angle: Wait, maybe \( b \) is equal to \( 118^\circ \) because they are vertical angles? Wait, no, wait. Wait, the vertical line is a straight line, so the angle between the vertical line and the slanted line: the angle \( 118^\circ \) and \( c \) are adjacent, so \( c + 118^\circ = 180^\circ \), so \( c = 180 - 118 = 62^\circ \)? Wait, no, maybe I got it wrong. Wait, let's re-examine.

Wait, the diagram: two lines intersect, one vertical, one slanted. The angle given is \( 118^\circ \) next to \( c \), and \( b \) is opposite? Wait, no, let's think about vertical angles and linear pairs.

First, angle \( b \) and the \( 118^\circ \) angle: are they vertical angles? Wait, no, if the vertical line is a straight line, then the angle \( 118^\circ \) and \( c \) are supplementary (linear pair), so \( c = 180 - 118 = 62^\circ \). Then, angle \( b \) and the \( 118^\circ \) angle: are they vertical angles? Wait, no, angle \( b \) and the \( 118^\circ \) angle—wait, maybe \( b \) is equal to \( 118^\circ \) because they are vertical angles? Wait, no, let's see: when two lines intersect, vertical angles are equal, and linear pairs are supplementary.

Wait, the vertical line is a straight line, so the angle between the vertical line and the slanted line: the angle \( 118^\circ \) and \( c \) are adjacent, so they form a linear pair, so \( c + 118^\circ = 180^\circ \), so \( c = 180 - 118 = 62^\circ \). Then, angle \( b \) and the \( 118^\circ \) angle: are they vertical angles? Wait, no, angle \( b \) and the \( 118^\circ \) angle—wait, maybe \( b \) is equal to \( 118^\circ \) because they are vertical angles? Wait, no, let's check the positions.

Wait, the two lines intersect, so the angle opposite to \( 118^\circ \) would be \( b \), so \( b = 118^\circ \), and the angle adjacent to \( 118^\circ \) (which is \( c \)) would be supplementary, so \( c = 180 - 118 = 62^\circ \). Yes, that makes sense. Because when two lines intersect, vertical angles are equal, so \( b \) is vertical to \( 118^\circ \), so \( b = 118^\circ \). And \( c \) is adjacent to \( 118^\circ \), forming a linear pair, so \( c = 180 - 118 = 62^\circ \).

Step1: Find \( b \)

Vertical angles are equal. The angle \( b \) and the \( 118^\circ \) angle are vertical angles, so \( b = 118^\circ \).
\[ b = 118^\circ \]

Step2: Find \( c \)

Angles on a straight line (linear pair) sum to \( 180^\circ \). The angle \( c \) and \( 118^\circ \) form a linear pair, so \( c + 118^\circ = 180^\circ \). Solving for \( c \):
\[ c = 180^\circ - 118^\circ = 62^\circ \]

Answer:

\( b = \boxed{118}^\circ \), \( c = \boxed{62}^\circ \)