Relationship between angle of banked road and normal force and its component

Question

Why are these two angles in the diagram below equal? I can't quite see their relationship or proof of why they are the same.

Answer 1

On flat ground, $N$ points straight up.

Now, tilt the ground. For $N$ to remain perpendicular to the ground, it must "tilt along" - it must as well be tilted equally much. Tilt the ground with $\theta$, and $N$ must as well tilt with $\theta$ in the same rotational direction (clockwise in your case).

Otherwise, if it was tilted with any other angle, it wouldn't be perpendicular anymore.

Answer 2

The angle between $f$ and the $x$-axis is equal to $\theta$ because they are both complementary to the angle between $N$ and the $x$-axis. The angle in the fourth quadrant is equal to $\theta$ because alternate interior angles are equal.