Question

find the measure of the missing angles.

Explanation:

Step1: Find \( h \)

Angles on a straight line sum to \( 180^\circ \). So \( h + 113^\circ = 180^\circ \), thus \( h = 180^\circ - 113^\circ = 67^\circ \).

Step2: Find \( g \)

\( g \) and \( 113^\circ \) are vertical angles (opposite angles when two lines intersect), so \( g = 113^\circ \).

Step3: Find \( m \)

Angles on a straight line sum to \( 180^\circ \). So \( m + 125^\circ = 180^\circ \), thus \( m = 180^\circ - 125^\circ = 55^\circ \).

Step4: Find \( k \)

\( k \) and \( 125^\circ \) are vertical angles, so \( k = 125^\circ \).

Answer:

\( h = 67^\circ \), \( g = 113^\circ \), \( m = 55^\circ \), \( k = 125^\circ \)