Manually post to search results page
Drupal core search result pages do not listen to URL Parameters or HTTP POST content. 
Instead, it takes the third part from the search/node/QUERY URL format, and shows results for QUERY.

This unfortunately makes it not possible to use a standard HTML form created without Drupal's form API. There are of course workarounds. 

Basically what we try to do is route the user's search query to the search/node path. I can see you are using Angular. You might be able to make it send the user to the proper path. 

Alternately, you can make Drupal listen to URL parameters or the HTTP post request content. 

https://www.drupal.org/project/query_parameters_to_url - this module I just found (and did not try personally) appears to rewrite URL parameters to a path query. I'm not sure this will work for search forms though. 

If not, you will have to create a custom module, and take over the search result page callback. Then, it can show appropriate results or call the old page callback function with the search query taken from alternative sources.