There is apparently a video game that came out that had Marty travelling to 1931 and meeting with a teenage Emmett Brown. Without further information that puts his DOB from 1912 to 1918, making him between 67 and 73 years old in 1985.
Before I did the research that found out about the video game I was guessing that his age was 70 in 1985. This is just simple supposition based on the fact that at the end of the first movie, he travels 30 years into the future (which would according to my guess make him exactly 100 years old). Again this was just guessing based on knowledge of the character and the idea that I believe it would personally appeal to anyone to travel to a time when they turned 100 years old.
If the video game is canon, then this guess would fit within canon as well, making him 16 years old (a teenager) during the video game. This would also make him only 40 years old during the events that take place in 1955, which seems to make him slightly younger than his appearances during that time, however Christopher Lloyd was born in 1938, making him only 47 when the first movie was released.
I haven't personally played the video game, so I am unsure as to whether his age is more definitively pinpointed in canon, so the most I can definitively say is between 67 and 73 years old during 1985. I would submit that I find it likely that his true age in 1985 was 70 years old.