Angle between planes

Question

If the angle between two planes is $\alpha$ , why is the angle between normal of the two planes is $\pi - \alpha$ ? Also Why angle between a line and normal to a plane is $\pi/2 -\alpha$ if angle between line and the plane is $\alpha$ ?

Answer 1

The normal vector is at an angle of $\frac{\pi}{2}$ with the plane. This may be a helpful diagram: .

If you take an angle $B$ to be the supplementary angle (angle between the two planes $> \frac{\pi}{2}$) to $A$ you can easily see why A = $\pi - B$

Answer 2

the normal to the plane always lies in a perpendicular plane....thus angle between the line and normal is less than the angle between the plane and line