Question

find the measure of the missing angles.
answer attempt 1 out of 2
b = \boxed{^circ} quad c = \boxed{^circ}

Explanation:

Step1: Find angle \( b \)

Angles on a straight line sum to \( 180^\circ \). So \( b + 85^\circ = 180^\circ \).
\( b = 180^\circ - 85^\circ = 95^\circ \)

Step2: Find angle \( c \)

Vertical angles are equal, or \( c \) and \( 85^\circ \) are vertical? Wait, no, \( c \) and \( 85^\circ \): Wait, \( b \) and \( c \) are adjacent? Wait, no, when two lines intersect, vertical angles are equal. The angle opposite \( 85^\circ \) is \( c \)? Wait, no, let's recheck. The angle \( b \) and \( 85^\circ \) are supplementary (straight line). Then \( c \) is vertical to \( 85^\circ \)? Wait, no, the angle adjacent to \( b \) and opposite to \( 85^\circ \) is \( c \). Wait, actually, when two lines intersect, vertical angles are equal. So the angle opposite \( 85^\circ \) is \( c \)? No, wait, the angle between the two lines: the angle \( 85^\circ \) and \( c \): Wait, no, let's see. The two lines intersect, so \( b \) and \( 85^\circ \) are supplementary (sum to \( 180^\circ \)), so \( b = 95^\circ \). Then \( c \) is vertical to \( 85^\circ \), so \( c = 85^\circ \)? Wait, no, wait. Wait, the angle \( c \) and \( b \) are supplementary? No, wait, when two lines intersect, the vertical angles are equal. So the angle opposite \( 85^\circ \) is \( c \), so \( c = 85^\circ \), and the angle opposite \( b \) is equal to \( b \). Wait, let's draw mentally: two lines crossing, forming four angles. One angle is \( 85^\circ \), its adjacent angle (on the straight line) is \( b \), so \( b = 180 - 85 = 95 \). Then the angle opposite \( 85^\circ \) is \( c \), so \( c = 85^\circ \), because vertical angles are equal.

Answer:

\( b = 95^\circ \), \( c = 85^\circ \)