Question 1022129
<pre>Here's another way to do it.

Think of the clock face being marked 0° at 12:00PM, 90° at
3:00, 180° at 6:00PM and 270° at 9:00PM.

Since there are 60 minute markers around the clock face they
are 360°/12 or 6° apart.

The numerals are 30° apart.

Then at 5:00PM the minute hand is at 0° and the hour hand is
at 150°, 30° less than 6:00PM. 

At 5:44PM the minute hand has turned through 44x6° or 264°
since 5:00PM, so the minute hand is at 264°.

But the hour hand has only turned 1/12th that many degrees or
only 1/12th of 264° or 22°, so at 5:44PM it's at 150°+22° or at
172°.

So the angle between them is 264°-172° or 92°.  

Edwin</pre>