Angles Everywhere

At 12:15 the two hands of the clock looks to be forming about a right angle i. e. 90 degree. but hour hand also keeps on moving further the moved portion of the hour hand has to be reduced from 90 degree. Now we have to find out the moved portion oh hour hand within 15 minute. Since an hour hand moves between two consecutive numbers i.e. 12th part of a circle (making a arc 30 degrees) when a minute hand moves one hour or 60 minutes or 360 degrees
Here in the problem minute hour moves 15 minutes i.e. one fourth portion of an hour . accordingly an hour hand also moves proportionately and it is one forth of 30 degrees which comes to 7.5 minutes Hence 90 -- 7.5 = 82.5 degree is the angle formed by clock at 12:15

At 12:15 the angle is 90 degree.

But in these 15 minutes the hour hand will also move by some angle.

Remember that the hour hand moves by 0.5 degree every minute.

Therefore, the hour hand will move by 0.5 x 15 = 7.5 degree.So the answer is 90-7.5 that is equal to 82.5 degrees.