What is the degree measure of the smaller angle between the hour hand and the minute hand of a clock at exactly \(2:45\) p.m. on a 12-hour analog clock?
Minute hand moves 6 degree per minute past 12 45 min then = 270 degrees
hour hand moves 1/2 degree per minute 165 min then becomes 82.5 degrees
the smaller angle is then 360 - 270 + 82.5 = 172.5 degrees
