What is the smaller angle formed by the minute and hour hands at 3:30pm?

75 degrees

Step-by-step explanation:

360/60=6 degrees per minute on a clock face

minute hand, from 12 o'clock position is 30 minutes so 30x6=180 degrees

hour hand, from 12 o'clock position is 17.5 minutes so 17.5x6=105 degrees

180-105=75 degrees

75 degrees.

Step-by-step explanation:

The angles between 2 consecutive  numbers on the clock are 360 /12 = 30 degrees.

The hour hand is half way between the 3 and 4 so this = 15 degrees,

So the required angle = 2*30 + 15

= 75 degrees.