What is the angle (in degrees) that a line with slope $m$ makes with the x-axis (x>=0)

Question

I have tried this many times, but all I have figured out is that if one line has slope $a$ and another line has slope $b$ then the ratio of the angles made with the y-axis is the same as the ratio of the two numbers.

Answer 1

Do you know that the slope of the line through the origin with angle $\theta$ (measured counterclockwise from the positive $x$-axis) is $\tan\theta$?

So the angle corresponding to slope $m$ would be $\tan^{-1}m$, which could be taken to lie in $(-90^{\circ},90^{\circ})$.