Question

find the measure of the missing angles.
answer attempt 1 out of 2
b = □° c = □°

Explanation:

Step1: Find the measure of angle \( b \)

Angles \( b \) and \( 146^{\circ} \) are supplementary (they form a linear - pair). The sum of angles in a linear - pair is \( 180^{\circ} \).
So, \( b+146^{\circ}=180^{\circ} \).
Subtract \( 146^{\circ} \) from both sides: \( b = 180^{\circ}-146^{\circ}=34^{\circ} \).

Step2: Find the measure of angle \( c \)

Angles \( c \) and \( 146^{\circ} \) are vertical angles. Vertical angles are equal.
So, \( c = 34^{\circ} \) (since \( c \) and \( b \) are also vertical angles, and we could also use the vertical - angle relationship with \( 146^{\circ} \) in another way. But since \( b = 34^{\circ} \) and \( c\) and \( b\) are vertical angles, \( c=b \)).

Answer:

\( b = 34^{\circ}\), \( c = 34^{\circ}\)