Since considering four-bar linkages is a useful tool in my research field, I happen to know of a paper that precisely solves what you want to do. George H. Martin published in 1958 in the journal Machine Design the paper "Four-Bar Linkages", the following equations are taken from that paper:
When you consider a four-bar linkage as shown below, then ...
Any parametric cad software can create a sketch and then measure the angle as driven.
onshape (browser based no need to install anything)
Also you can look at geogebra-geometry which is something that combines 2d algebra and geometry.
I found a related question that is effectively asking the same question. This is typically known as a four bar linkage (I only drew three in my diagram since the 4th bar is static). As far as I can see, you can derive a trigonometric relationship between the angles, but it isn't exactly simple.