The rotation of gear $\mathrm{B}$ is found from the angle of twist in shaft $\left(1\right)$:

$$\begin{gathered} {\mathrm{\varphi }}_1={\mathrm{\varphi }}_{\mathrm{B}}-{\mathrm{\varphi }}_{\mathrm{A}} \\ \therefore {\mathrm{\varphi }}_{\mathrm{B}}={\mathrm{\varphi }}_{\mathrm{A}}+{\mathrm{\varphi }}_1=0 \mathrm{rad}+(-0.050724 \mathrm{rad})=-0.050724 \mathrm{rad} \end{gathered}$$

Recall that the sign convention for rotation angles is based on the right-hand rule. Here, the rotation angle of gear $\mathrm{B}$ is negative. Thus, if you wrap the fingers of your right hand in the direction that gear $\mathrm{B}$ rotates, your thumb points in the $\mathrm{-x}$ direction.