To add to the other responses, when the French were developing their “metric” system following the French Revolution, they did come up with [a 10-based system for angles](https://en.wikipedia.org/wiki/Gradian).
Rather than splitting a circle into 100, they split a right-angle into 100. One gradian, or gon, if 1/400 of a full turn (or 9/10ths of a standard degree). While it didn’t take off as much as other decimal measurements, it is still used – particularly in some areas of surveying and mining, especially by the French. Many scientific calculators will have an option to give angles in gradians (along with degrees and the mathematically-more-satisfying radians).
They also developed a decimal system for time; from 1794 to 1800 the French Republican calendar divided the day into 10 hours, with each hour having 100 minutes, and each minute having 100 seconds (giving a slightly shorter second, one decimal second lasting only 0.86 conventional seconds).
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