A picture would certainly help in this case. I need to assess the situation visually.

I would cut out the dead wood anyway whilst you can see where the dead branches are. It is not unusual for some species of mature trees to shed old branches. Some times there has been a problem with the vessels that carry the water around so it is no longer viable. The causes are many, fungal is the main culprit.

A photo would certainly help in seeing if there is an overall problem with the tree.

Welcome to GoY too :o)