Angle perpendicular lines and x-axis Let's say we have a line $L$ with positive slope that intersects $(0,0)$ and makes an angle of $\theta&lt;90^\circ$ with the $x$-axis ("on top" of the x-axis, i.e. the angle is in quadrant 1). Given a line perpendicular to $L$ going through quadrant 1, what is the angle this line forms with the x-axis?

The answer, intuitively, seems to be $90-\theta$. But I don't know how to prove it.
You are right. To prove it just consider the right triangle formed by $x$ axis, line $L$ and the second perpendicular to $L$, then since the sum of the internal angles adds up to $180°$ the angle that the perpendicular line forms with the x-axis is $90°-\theta$.
The two lines and the x-axis form a triangle. One angle is $\theta$ and one is $90^{\circ}$. 

The last angle can then only be ....