### Instruction: What is the number of degrees in the measure of the smaller obtuse angle formed by the hands of a standard clock at 2:48pm?### Response: To solve this problem, I need to find the angle between the hour hand and the minute hand at 2:48pm.
I know that the hour hand moves 360 degrees in 12 hours, so its angular speed is 30 degrees per hour.
Similarly, the minute hand moves 360 degrees in 60 minutes, so its angular speed is 6 degrees per minute.
At 2:48pm, the hour hand has moved 2 hours and 48 minutes from the 12 o'clock position, so its angle is 2 times 30 plus 48 times 0.5, which is 84 degrees.
The minute hand has moved 48 minutes from the 12 o'clock position, so its angle is 48 times 6, which is 288 degrees.
The difference between these two angles is 288 minus 84, which is 204 degrees.
However, this is not the smaller obtuse angle, since it is larger than 180 degrees.
To find the smaller angle, I need to subtract 204 from 360, which gives 156 degrees.