Measure the acute angle using two plane normals

Use the normals $\mathbf n_1=(1,-1,-1)$ and $\mathbf n_2=(1,-1,-2)$. As in the printed solution, let their angle be $\theta$:

$\begin{aligned}\mathbf n_1\cdot\mathbf n_2&=1+1+2=4,\\|\mathbf n_1|&=\sqrt3,\quad |\mathbf n_2|=\sqrt6,\\4&=\sqrt3\sqrt6\cos\theta,\\\theta&=\cos^{-1}\!\left(\frac4{\sqrt3\sqrt6}\right).\end{aligned}$

This gives $19.4712\ldots^\circ=0.339836\ldots$ radians. The normal angle is acute, so it is also the acute angle between the planes. Round separately in the required units to get the two printed answers. Plane constants locate the planes; they do not change this angle.