The answer is 90.5.

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Trung Le , you should mention that the answer is in degree.

At $11:00$ the two hands are $30^\circ$ apart. Let the hour-hand and minute-hand move $\theta_h$ and $\theta_m$ in $11$ minutes respectively. Then, the smaller angle between the two hands is given by:

$\begin{aligned} \theta & = 30 - \theta_h + \theta_m \\ & = 30 - \frac{11}{60} \times 30 + \frac{11}{60} \times 360 \\ & = 30 - 5.5 + 66 \\ & = \boxed{90.5} \end{aligned}$