Yes masks work against respiratory viruses, here is how and the studies, plural to prove it.

 It's been over a year since I argued with a close friend who was at one point a respiratory therapist on this. 
He correctly stated that viruses are too small for any mask fiber, that is true, what he missed and I tried to explain to him unsuccessfully at the time, is that they are transmitted on water particles, which are not to small and can get caught in fibers or membrane. 
To note, not all masks are the same, nevertheless without wasting anymore breath here are the multiple studies from various organizations to prove that yes, they can and do work. 
The easiest way to understand this is to put on a mask and sneeze what comes out? 
Some will of course, but even then particles distance are drastically reduced which is still a form of success. 
For Medical Professionals working in a high risk environment quality of mask is paramount do to constant exposure. 


A rapid systematic review of the efficacy of face masks and respirators against coronaviruses and other respiratory transmissible viruses for the community, healthcare workers and sick patients - PubMed (nih.gov)

EPA Researchers Test Effectiveness of Face Masks, Disinfection Methods Against COVID-19 | US EPA


Face masks against COVID-19: Standards, efficacy, testing and decontamination methods (nih.gov)


Do cloth masks actually work? | MIT Medical



Large Study Confirms Masks Work to Limit COVID-19 Spread (webmd.com)



Still Confused About Masks? Here’s the Science Behind How Face Masks Prevent Coronavirus | UC San Francisco (ucsf.edu)