Question

answer attempt 1 out of 2
$g=square^{circ}$ $h=square^{circ}$
$k=square^{circ}$ $m=square^{circ}$

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle \(m\) and the \(121^{\circ}\) angle are vertical angles, so \(m = 121^{\circ}\).

Step2: Use linear - pair property

A linear - pair of angles sums to \(180^{\circ}\). For the linear pair with the \(121^{\circ}\) angle and \(k\), we have \(k+121^{\circ}=180^{\circ}\), so \(k = 180^{\circ}-121^{\circ}=59^{\circ}\).

Step3: Use vertical - angle property again

Angle \(h\) and the \(119^{\circ}\) angle are vertical angles, so \(h = 119^{\circ}\).

Step4: Use linear - pair property again

For the linear pair with the \(119^{\circ}\) angle and \(g\), we have \(g + 119^{\circ}=180^{\circ}\), so \(g=180^{\circ}-119^{\circ}=61^{\circ}\).

Answer:

\(g = 61\)
\(h = 119\)
\(k = 59\)
\(m = 121\)