Angle between hour and minute hand at 2:42

Question

Angle made by hour hand:

       for 2 hours: 2*30 = 60

       for 42 mins: (42/60) * 30 = 21

       Total angle made by hour hand is: (60 + 21)= 81 degrees

Angle made by minute hand:

       for 42 min: 42*6 = 252 

       Total angle made by minute hand is: 252 degrees

The angle between the minute and hour hand is: (252-81) = 171 degrees

My question is about "why is 171 degrees a wrong answer" and the correct answer is 189 degrees

Answer 1

Here is the right image of the clock. See the angle between hour and minute hand is measured in a counterclockwise manner, hence it is more than $180^{\circ}$.

Answer 2

The question asks for the angle between the hour and the minute, rather than the angle between the minute and the hour. See the diagram below for the discrepancy.