Question

answer attempt 2 out of 2

$g=61^{circ}$ $h=61^{circ}$
$k=121^{circ}$ $m=59^{circ}$

Explanation:

Step1: Find the value of \( g \)

Adjacent angles on a straight line sum to \( 180^{\circ} \). So \( g+119^{\circ}=180^{\circ} \), then \( g = 180^{\circ}-119^{\circ}=61^{\circ} \).

Step2: Find the value of \( h \)

Vertical angles are equal. \( h \) and \( g \) are vertical angles. So \( h = g=61^{\circ} \).

Step3: Find the value of \( k \)

Vertical angles are equal. \( k \) and \( 121^{\circ} \) are vertical angles. So \( k = 121^{\circ} \).

Step4: Find the value of \( m \)

Adjacent angles on a straight line sum to \( 180^{\circ} \). So \( m + 121^{\circ}=180^{\circ} \), then \( m=180^{\circ}-121^{\circ}=59^{\circ} \).

Answer:

\( g = 61^{\circ}\), \( h = 61^{\circ}\), \( k = 121^{\circ}\), \( m = 59^{\circ}\)