ANSWER
[tex]2.44\text{ }rad[/tex]EXPLANATION
First, let us make a sketch of the clock:
We have that for a minute hand:
[tex]1\text{ }min=6\degree[/tex]For hour hand:
[tex]1\text{ }min=0.5\degree[/tex]The hour and minute hand have their origin at 12.
At 11:20, the minute hand had moved 20 mins. This means that:
[tex]20\text{ }min=20*6=120\degree[/tex]The hour hand had moved at 11 (and 20 mins more), which means:
[tex]\begin{gathered} 11*60\text{ }min+20\text{ }min \\ \Rightarrow660\text{ }min+20\text{ }min \\ 680\text{ }min \end{gathered}[/tex]Hence, in 680 mins:
[tex]\begin{gathered} 680*0.5 \\ \Rightarrow340\degree \end{gathered}[/tex]Therefore, the angle formed between 11 and 12 at 11:20 is:
[tex]\begin{gathered} 360-340 \\ \Rightarrow20\degree \end{gathered}[/tex]Hence, the angle formed at 11:20 is:
[tex]\begin{gathered} 120\degree+20\degree \\ 140\degree \end{gathered}[/tex]Now, let us convert to radians:
[tex]\begin{gathered} 1\degree=\frac{\pi}{180}rad \\ 140\degree=140*\frac{\pi}{180}=2.44\text{ }rad \end{gathered}[/tex]That is the obtuse angle formed in radians.
