Question

question
find the measure of the missing angles.
answer attempt 3 out of 5
b = \\(\square^\circ\\) \quad c = \\(\square^\circ\\)

Explanation:

Step1: Find angle \( c \)

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

Step2: Find angle \( b \)

Vertical angles are equal, and also \( b \) and \( 85^\circ \) are vertical angles? Wait, no, \( b \) and \( 85^\circ \)? Wait, actually, \( b \) and \( 85^\circ \) are vertical angles? Wait, no, looking at the diagram, \( b \) and \( 85^\circ \): Wait, no, \( c \) and \( b \) are adjacent? Wait, no, let's correct. Angles on a straight line: \( c + 85^\circ = 180^\circ \) (step1). Then, \( b \) and \( 85^\circ \) are vertical angles? Wait, no, vertical angles are opposite. Wait, actually, \( b \) and \( 85^\circ \) are vertical angles? Wait, no, the angle opposite to \( 85^\circ \) is \( b \)? Wait, no, let's see: when two lines intersect, vertical angles are equal. So the angle opposite to \( 85^\circ \) is \( b \), so \( b = 85^\circ \)? Wait, no, wait the diagram: the two lines intersect, forming angles. So angle \( b \) and the \( 85^\circ \) angle: are they vertical angles? Wait, maybe I made a mistake. Wait, let's re-examine. The angle \( c \) and \( 85^\circ \) are supplementary (sum to \( 180^\circ \)), so \( c = 95^\circ \). Then, angle \( b \) and \( 85^\circ \): are they vertical angles? Wait, no, angle \( b \) and \( c \) are supplementary? Wait, no, when two lines intersect, adjacent angles are supplementary. So angle \( b \) and \( c \) are supplementary? Wait, no, let's draw mentally: two lines intersect, so four angles. One angle is \( 85^\circ \), its adjacent angle is \( c \) (supplementary, so \( c = 95^\circ \)), then the angle opposite to \( 85^\circ \) is \( b \), so \( b = 85^\circ \), and the angle opposite to \( c \) is equal to \( c \). Wait, that makes sense. So vertical angles: opposite angles are equal. So \( b = 85^\circ \), \( c = 95^\circ \).

Wait, let's confirm:

• \( c + 85^\circ = 180^\circ \) (linear pair), so \( c = 95^\circ \).
• \( b \) and \( 85^\circ \) are vertical angles, so \( b = 85^\circ \).

Yes, that's correct.

Answer:

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