Question

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

Explanation:

Step1: Find angle \( b \)

Angle \( b \) and the \( 58^\circ \) angle are supplementary (they form a linear pair), so their sum is \( 180^\circ \).
\[
b + 58^\circ = 180^\circ
\]
\[
b = 180^\circ - 58^\circ = 122^\circ
\]

Step2: Find angle \( c \)

Angle \( c \) and the \( 58^\circ \) angle are vertical angles (opposite angles formed by intersecting lines), so they are equal.
\[
c = 58^\circ
\]
Or, angle \( c \) and angle \( b \) are supplementary, so:
\[
c + b = 180^\circ
\]
\[
c = 180^\circ - 122^\circ = 58^\circ
\]

Answer:

\( b = 122^\circ \), \( c = 58^\circ \)