It's not actually known who invented the protractor. Many people believe that Thomas Blundeville may have invented it, but as there were many different mathematicians writing about similar tools at the same time period (circa 1589), it's not possible to tell who coined the idea first.
The protractor is over 500 years old, and was initially used in map preparation and navigational charts. This wasn't the protractor's final form, however, and a more complex protractor was invented by Joseph Huddart in 1801. This became known as the three-arm protractor, and is made of a circular scale that's connected to three arms.
Today, protractor's are used in schools around the world, and have become an item that most people won't think about in their daily lives. For sailors of the past, however, protractor's were an integral part of navigation plotting.