What 57.295 degrees mean to you

Question

I've just calculated that one radian is equals 57.295.. degrees, does this degree have special property instead the fact that it is just a degree that define radian in degree

Answer 1

Radians and degrees are defined so that $2\pi$ radians is $360$ degrees. So $1$ radian is precisely $\frac{180}{\pi}$ degrees, which is the number you see there.

Answer 2

$57.295\dots$ is the number that, when multiplied by $2\pi$, yields $360$. There is absolutely nothing "special" about this number.

---

The only "meaning" behind a degree is "one $360$-th of a full circle", while a radian means "one $2\pi$-th of a full circle". From these two things, it already follows that $2\pi\mathrm {radians} = 360\mathrm{degrees}$, or, dividing by $2\pi$, that $$1\mathrm{radian} = \frac{360}{2\pi}\mathrm{degrees}$$

Note that while $\pi$ is a number with a certain significance (and therefore, measuring in radians makes inherent sense), $360$ is a completely arbitrary number that we decided to use a long time ago (measuring in degrees is therefore just a matter of convention).