Why do we use degrees?

Question

I see a lot of people who ask why we use radians instead of degrees. But why do we use degrees instead of radians. In the cases we use degrees instead of radians, what convenience does it bring? The only benefit I see is eyeballing small angles, but that's probably because I don't measure angles everyday. So, what are the practical benefits?

Answer 1

Historical precedent and continuity. You can read about the history in the link in the comments, but it's really just tradition.

Answer 2

$360$ has lots of nice divisors.

Answer 3

Having 360 degrees be a full circle may seem a bit odd of a number to use, but it's actually very practical. If we find the prime factors of it, then we can understand why it is useful and practical. $360 \rightarrow 180 \rightarrow 90 \rightarrow 45 \rightarrow 15 \rightarrow 5 \rightarrow 1$

$\ \ \ \ \ \ \div2 \ \ \ \ \div2 \ \ \ \ \div2 \ \ \ \div3 \ \ \ \div3 \ \ \div5$

$ 2^3 \times 3^2 \times 5^1 = 360$

We can divide this number by $2$ 3 times, divide by $3$ 2 times and divide by $5$ 1 time and still have it be whole! Halves, thirds and fifths are the fractions we most commonly come across and use due to them being the lowest prime numbers, and we generally use lower prime numbers more than higher ones (that's why you can divide 3 times by $2$ and only once by $5$). This is what makes the number convenient and practical.

Answer 4

Number of days in a year is likely the reason. If the year had 400+/- days, we'd probably have a 400 degree standard.