Question

find the measure of the missing angles.

Explanation:

Step1: Find angle \( b \)

Angle \( b \) and the \( 62^\circ \) angle are supplementary (they form a linear pair), so their sum is \( 180^\circ \).
\[
b + 62^\circ = 180^\circ
\]
\[
b = 180^\circ - 62^\circ = 118^\circ
\]

Step2: Find angle \( c \)

Angle \( c \) and the \( 62^\circ \) angle are vertical angles (opposite angles formed by intersecting lines), so they are equal.
\[
c = 62^\circ
\]
Or, angle \( c \) and angle \( b \) are supplementary, so:
\[
c + b = 180^\circ
\]
\[
c = 180^\circ - 118^\circ = 62^\circ
\]

Answer:

\( b = 118^\circ \), \( c = 62^\circ \)