Out of the box Excel has no support for what you are asking. There might be plugins around that help with this, but instead I'd like to offer a little work-around:
You can format numbers as time to get Excel (and probably OOo and LibreOffice) to display and calculate values that as you need with the correct divisions, bases, etc.
Using the following custom format (Excel, OOo and LibreOffice will have equivalents but I don't have a copy to hand to test) will render them with the correct symbols as well. The
[h] prevents the hour resetting to zero as it reaches 24 allowing arbitrarily large angles. If you'd like leading zero's then just double-up each letter.
[h]º m' s\"
These can be added together, etc, as necessary (they are just numbers underneath, after all). However, this will only work if the final result is positive; Excel will not will render negative times.
If you need to convert this value in to a decimal degrees value, you just need to multiply by 24, because a "day" in Excel time format has a value of 1 (so an hour is 1/24th, etc).
Just make sure the cell this formula goes in has normal formatting - not time:
Alternatively, you can also extract specific components from the time value by using the following:
=INT(A1*24) returns degrees
=MINUTE(A1) returns minutes
=SECOND(A1) returns seconds