Use the formula
[tex]{\omega_f}^2-{\omega_i}^2=2\alpha\Delta\theta[/tex]
[tex]\implies\left(13.5\dfrac{\rm rad}{\rm s}\right)^2-\left(22.0\dfrac{\rm rad}{\rm s}\right)^2=2\alpha(13.8\,\mathrm{rad})[/tex]
[tex]\implies\alpha=-10.9\dfrac{\rm rad}{\mathrm s^2}[/tex]
so the magnitude is 10.9 rad/s^2.
