The answer for How do you know a straight line forms an angle of 180°? is (by users in the post) that A straight line, by definition, is $180^\circ$.
I wonder why mathematicians don't chose any other number but $180$ for the definition of a straight line.
On
It is that way for historical reasons.
Babylonians used to count with an sexagesimal system (base 60 instead of base 10).
And they chose straight line as three of their units.
Also for defining $\pi$, Euler used different notations, like we use $\theta$ these days for noting any angle, sometimes $\pi$ refered as the value $\pi$, sometimes as $2 \pi$. So once again, it's for historical reasons that we picked these choices.
Feel free to imagine other conventions, but it's very unlikely other mathematicians will understand.
On
Your question is more, why have mathematicians chosen $360^\circ$, as a straight line is just half of a full turn. $360^\circ$ is chosen because it has a lot of factors (1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, ...), a more natural measurement of angle is Radians, in which a straight line is $\pi$ and a full turn is $2\pi$.
Have a read of this:
Mathematicians don't use angles at all. Historically because the solar cycle was close to $360$ days and babylonians used a base $60$ number system so $360$ was used to describe a full cycle similar to the solar year. Typically definitions are meant to match intuition, so a straight line should be straight in the colloquial sense and only one angle can represent that.