The angles of twist in shafts $\left(1\right)$ and $\left(2\right)$ are computed as follows:

$$\begin{gathered} {\mathrm{\varphi }}_1=\frac{{\mathrm{T}}_1{\mathrm{L}}_1}{{\mathrm{J}}_1{\mathrm{G}}_1} \\ =\frac{(-43.768 \mathrm{lb}-\mathrm{ft})(36 \mathrm{in}.)(12 \mathrm{in.}/ft)}{(0.031063 {\mathrm{in.}}^4)(12,000,000 \mathrm{psi})} \\ =-0.050724 \mathrm{rad} \end{gathered}$$

$$\begin{gathered} {\mathrm{\varphi }}_2=\frac{{\mathrm{T}}_2{\mathrm{L}}_2}{{\mathrm{J}}_2{\mathrm{G}}_2} \\ =\frac{(131.303 \mathrm{lb}-\mathrm{ft})(96 \mathrm{in}.)(12 \mathrm{in.}/\mathrm{ft})}{(0.239684 {\mathrm{in.}}^4)(\mathrm{12,000,000} \mathrm{psi})} \\ =-0.052590 \mathrm{rad} \end{gathered}$$