There are simply many different distributions of LaTeX or TeX and each of these have different default symbol sets and often additional packages. What you copy from one environment does not always look the same in that environment where you paste code. Each latex renderer can have different versions.

First you need to know what latex renderer (tex filter) your site is using - Mimetex, TexLive, MikTeX, OzTeX, TeTeX,... or for example cdn MathJax with script tags (and given tokens) in Additional HTML in site administration. MathJax supports both \angle and \sphericalangle symbols http://docs.mathjax.org/en/latest/tex.html#s

If you are using a local LaTeX (for example TexLive) you can add additional packages to settings of tex filter - tex preamble, see for example https://moodle.org/mod/forum/discuss.php?d=152292

If you can't change your latex renderer and can't use several latex renderers (tex filter AND MathJax) you can also copy and paste images from what ever source or math editor... with image plugin in editor toolbar like Al did with his example sphericalangle.

If you check https://moodle.org/mod/forum/discuss.php?d=193064 adding script tags for MathJax is not a complex thing to do. As an administrator of your site you can change the configuration of MathJax, select proper tokens for inlinemaths and use mathJax with or without tex filter, with local files or with cdn files http://docs.mathjax.org/en/latest/configuration.html