The first thing you need for that Asymptote code is a module called
olympian, that can be downloaded here: http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=165767 This adds support for
anglemark and more.
It is the file attached to the first post in that thread. Save it as
olympian.asy in the same folder as your
.tex file. To use the module, add
import olympian; to the Asymptote code.
Next, you want to draw the arcs, so instead of having the
anglemark within the labels, it seemed necessary to have it in a
draw command, so
label("$\ \ \ \ \ \ \ 30^\circ$",D,SE);;
label("$80^\circ \ \ \ $",E,W);
E is the point
The default size of the arc is quite small, it can be increased by adding
Adjust the value to your needs.
I don't know what is the best to label angles, but I've added a suggestion:
This label is placed at
35 units in the
-7 degrees. The
\small command makes the font a little smaller. Perhaps not necessary, but it was a bit cramped in the top left corner.
When compiling the above with
pdflatex, a file called
<filename>-1.asy is generated. To generate the image, this has to be compiled with the Asymptote program, so run
from a command line/terminal. Compile your
.tex file again with
pdflatex and the image should be included in your document.
You could also open the
.asy in TeXshop file and compile it with the Asymptote engine, mentioned by Alan Munn in a comment.
Finally, it should be possible to do this compilation automatically with
latexmk, but I wasn't successful in my attempts (I probably did something wrong).
Output of above code