The difference between the hour and minute hand of a clock is given by |30H−5.5m| Here H is the current hour and m represents the number of completed minutes in the current hour. In the given time frame of 2: 30 to 3: 00 pm. At 2 : 30 pm the angle =|30.2−5.5.30|=105degrees At 3: 00 pm the angle |30.3−5.5.0|=90degrees The function of 30.H−5.5.m|= constantly increases as the value of m increases from 31,32................59 Because of the modulus function, the net value of the function remains positive Between 2: 30 to 2: 59 the angle is constantly increasing. The minimum value is 2: 30 which is equal to 105degrees which is greaterthan the 90degrees when the time is 3: 00. Hence 90degrees is the minimum angle.