character encoding confusion

[patrol]

I created a program in C that requires the degree symbol. The mode
line indicates that Emacs is using the Latin-1 character encoding.
According to Latin-1 encoding tables, the degree symbol is encoded as
decimal 176, so that's what I used in my code. But when the character
printed, it wasn't the degree symbol; it was a "shaded box" looking
thing. Then I looked at an ASCII table here (http://
www.asciitable.com/), and it says that 176 is indeed the shaded box
that was printed in my program, and the degree character was decimal
248. So I used 248 in my code, and I got the degree symbol I wanted.

But all this leaves me with the question that if Emacs was supposedly
encoding the file in Latin-1, why doesn't the code for the degree
symbol match up with the Latin-1 table? Why does it instead match up
with some non-standard "extended" ASCII that I just happened to come
across.

Can anyone shed light on this?
Thanks