At 3: 30 p. m. the angle between the hands of a
clock is

Well, the "hour" hand is 3.5*30=105 degrees from the "12" marking (30 degrees per hour), while the "minute" hand is 30*6=180 degrees from the "12" marking (6 degs per minute). The difference, that is, 75 degrees, is our angle. The other difference would have been over 180, which is not important for us.