How Do Angles Relate in Inclined Plane Physics?

[Dustinsfl]

In physics, when we draw a block on an incline, we know that the angles are the same see image:

Incline angle = angle formed by Mg, M, F_2

I can't recall what geometry properties allows us to make this statement.

 

[Deveno]

Imagine drawing a horizontal line through where your 2 blue vectors originate.

Since $F_2$ and the incline are perpendicular, if the angle of the incline is $\theta$, the angle between the horizontal line (going clockwise) and $F_2$ is $90 - \theta$.

Since the horizontal line and vector $Mg$ are also perpendicular the angle between the horizontal line and $F_2$ and the angle between $F_2$ and $Mg$ must sum to 90, so if the angle between $Mg$ and $F_2$ is called $\psi$, we have:

$\psi + 90 - \theta = 90$
$\psi - \theta = 0$
$\psi = \theta$.