k) $40^{\circ} 20^{\circ}: 2$
$55^{\prime \prime} \quad \operatorname{li} 45^{\circ} 20^{\prime}: 4$

Step 1 ：Given the angles in degrees, minutes, and seconds, we first need to convert them to decimal degrees.

Step 2 ：For the first part, we have \(40^\circ 20^\prime\). This can be converted to decimal degrees by adding the minutes divided by 60 to the degrees. So, \(40 + \frac{20}{60} = 40.33^\circ\).

Step 3 ：We are then asked to divide this result by 2, so \(\frac{40.33}{2} = 20.17^\circ\).

Step 4 ：For the second part, we have \(45^\circ 20^\prime 55^\prime\prime\). This can be converted to decimal degrees by adding the minutes divided by 60 and the seconds divided by 3600 to the degrees. So, \(45 + \frac{20}{60} + \frac{55}{3600} = 45.35^\circ\).

Step 5 ：We are then asked to divide this result by 4, so \(\frac{45.35}{4} = 11.34^\circ\).

Step 6 ：\(\boxed{20.17}\) and \(\boxed{11.34}\) are the final answers.