Can you build muscle doing high rep sets for example sets of 15 to 20 reps?
Absolutely.
But what the actual optimal training range with regard to sets and reps is (i.e. whether you respond more to heavy weight, lower volume or lighter weight, higher volume) for you is, will for the most part, depend on your genetics.
I’ve been training for over 40 years now. After the first year or so, I realised that anything less than 15 reps/set & 10–20 sets per bodypart didn’t work or make much sense to me. I didn’t get bigger or stronger with heavy, low rep work. All I got was injuries, frustration and bouts of tendonitis.
True, at first I had a little trouble with some of my mates, who loved to lift heavy and were a little disgusted with my ‘’pansy-assed attitude’’. Now, after most of them have hit middle- age, it is hard to find them in the gym any more. They are not there from being permanently injured out, or due to loss of the necessary motivation because, as they got older, it got harder and they couldn’t lift as heavily as easily and as pain-free as they once did.
In recent years, genetic testing has become affordable. Now, whether you think it is quite there as useful scientific reality or not, is another matter. I happen to think it is. I think that, interpreted properly it is well worth the time, effort and cost…as long as you take the resulting data with a grain (or more) of salt.
A couple of years ago, I had some genetic testing done and used several providers to double and triple check the outcomes. Results came back with data which generally had a high degree of agreement, indicating that I had a peculiar lack of the genes associated with strength, power, tendon integrity and fast-twitch muscle fibres. On the other hand, I was pretty richly supplied with genes relating to slow-twitch fibre volume, endurance, high IGF levels, nerve modularity, capacity for hyperplasia and other interesting qualities that might indicate a stronger endurance/aerobic orientation rather than strength and power orientation. Odd for a bodybuilder, nevertheless true for me.
Which, of course, many years of experience, trial and error and doing-it-the-hard-way had already taught me.

Cool !