What would be the smaller of the two angles formed by the hour hand and the minute hand at 3:47 p.m.?

The minute hand moves 6 degrees per minute. (That’s 360 degrees divided by 60 minutes)

The hour hand moves one-twelfth that, or $$\frac{1}{2}$$ degree per minute.

So the angle between the minute and hour hand increases by 5.5 degrees every minute.

The minute and hour hand start together at noon.

It takes 227 minutes(60+60+60+47) to get to 3:47 . So in this time, the angle between the hour and minute hand has increased $$227\times 5.5$$ degrees.

$$227\times 5.5$$= 1248.5 degrees.

Which is the same as 168.5 degrees.(1 cicrle is 360 so in 1248.5 deg  there are 3 circle and 168.5 deg left)