Question

find the measure of the missing angles.

Explanation:

Step1: Find angle \( h \)

Angles \( h \) and \( 123^\circ \) are supplementary (they form a linear pair), so their sum is \( 180^\circ \).
\[
h + 123^\circ = 180^\circ
\]
\[
h = 180^\circ - 123^\circ = 57^\circ
\]

Step2: Find angle \( g \)

Angles \( g \) and \( 123^\circ \) are vertical angles (opposite angles formed by intersecting lines), so they are equal.
\[
g = 123^\circ
\]
(Alternatively, \( g \) and \( h \) are supplementary, but vertical angles is more direct here.)

Step3: Find angle \( m \)

Angles \( m \) and \( 81^\circ \) are supplementary (linear pair), so:
\[
m + 81^\circ = 180^\circ
\]
\[
m = 180^\circ - 81^\circ = 99^\circ
\]

Step4: Find angle \( k \)

Angles \( k \) and \( 81^\circ \) are vertical angles, so they are equal.
\[
k = 81^\circ
\]
(Alternatively, \( k \) and \( m \) are supplementary, but vertical angles is simpler.)

Answer:

\( h = 57^\circ \), \( g = 123^\circ \), \( m = 99^\circ \), \( k = 81^\circ \)