Question

At what angle are the hands of a clock inclined at 25 minutes past 5?

Answer 1

The angle between the minute and the hour hand at five o'clock is 150${}^o$.
In 1 minute the angle changes by 5.5${}^o$.
So, in 25 minutes the angle changes by $5.5\times 25={137.5}^o$.
Thus, the angle between the two hands at 5:25 is ${150}^o-{137.5}^o={12.5}^o.$