The angle between the resultant contact force and the normal force...

Let $N$ be the normal force and $f$ be the force of friction between the two bodies.

The resultant contact force makes an angle $\lambda$ with the normal force. From the geometry of the forces, we have:

$\tan \lambda = \dfrac{f}{N}$

For static friction, the frictional force satisfies the inequality $f \leq \mu N$, where $\mu$ is the coefficient of static friction.

Substituting this into the equation for $\tan \lambda$, we get:

$\tan \lambda \leq \dfrac{\mu N}{N}$

$\tan \lambda \leq \mu$

Taking the inverse tangent on both sides, we obtain:

$\lambda \leq \tan^{-1} \mu$