Question

find the measure of the missing angles. answer attempt 1 out of 3 ( g=square^{circ} ) ( h=square^{circ} ) ( k=square^{circ} ) ( m=square^{circ} )

Explanation:

Step1: Find \( g \)

Use the fact that adjacent angles on a straight line sum to \( 180^{\circ} \).
\( g=180^{\circ}-118^{\circ} \)
\( g = 62^{\circ} \)

Step2: Find \( h \)

\( h \) and \( 118^{\circ} \) are adjacent angles on a straight line. But \( h \) and \( g \) are also adjacent. Since \( g = 62^{\circ} \), and \( h+g=180^{\circ} \), \( h = 118^{\circ} \) (alternatively, vertical - angle concept: \( h \) and \( 118^{\circ} \) are vertical angles, so \( h=118^{\circ} \))

Step3: Find \( k \)

Using the adjacent - angles - on - a - straight - line property (\( k + 133^{\circ}=180^{\circ} \))
\( k=180^{\circ}-133^{\circ} \)
\( k = 47^{\circ} \)

Step4: Find \( m \)

\( m \) and \( 133^{\circ} \) are adjacent angles on a straight line. Also, \( m \) and \( k \) are adjacent. Since \( k = 47^{\circ} \), and \( m + k=180^{\circ} \), \( m = 133^{\circ} \) (or vertical - angle concept: \( m \) and \( 133^{\circ} \) are vertical angles, so \( m = 133^{\circ} \))

Answer:

\( g = 62^{\circ}\), \(h = 118^{\circ}\), \(k = 47^{\circ}\), \(m = 133^{\circ}\)