The torques in shafts $\left(1\right)$ and $\left(2\right)$ were determined previously as:

$$\begin{gathered} {\mathrm{T}}_1=43.768 \mathrm{lb}-\mathrm{ft} \\ {\mathrm{T}}_2=131.303 \mathrm{lb}-\mathrm{ft} \end{gathered}$$

While only the torque magnitudes are necessary to compute the shear stress magnitudes in each shaft, the proper signs for ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ must be determined before the rotation angle of gear $\mathrm{D}$ with respect to flange $\mathrm{A}$ can be calculated. The signed values of ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ will be used to computes the angles of twist in shafts $\left(1\right)$ and $\left(2\right)$.