What angle does minute hand and hour hand clock inclined to each other at $2:25$ What angle does minute hand and hour hand clock inclined to each other at $2:25$
My Attempt:
The hour hand of a clock rotate throufh an angle of $30°$ in $1$ hour,
So,
At $2$o'clock, $2$ hrs$\equiv 60°$
Again,
The minute hand of a clock rotate through an angle of $6°$ in $1$ minute.
So, At $2:25$, i.e, $25$min$\equiv 150°$
What should I do further?
 A: You're correct in thinking that the minute hand will be at 150°, but the hour hand moves from 2:00 to 2:25, no?
You can think about 2:25 as being 2.416666 hours. Thus, 2.41666 x 30° = 72.5°.
So, minute hand at 150°, hour hand at 72.5°, what is the angle between the two?
A: Time 2 hrs 25 minutes. Converting into hours $2\frac{25}{60} = 2 \frac5{12} = \frac {29}{12}$
Angle made by hour hand in $\frac {29}{12}$ hrs $= \frac{360}{12} \times \frac{29}{12} = \frac {145}{2} = 72.5°$
Angle made by minute hand in 25 min $=  \frac{360}{60} \times 25 = 150°$
Difference in angle $= 150° - 72.5° = 77.5°$
A: I'd envision it like so:

The blue arc represents a rotation of $2/12$ of a full rotation, or $60^{\circ}$ since a full rotation is $360^{\circ}$.
The green segment represents a rotation in the opposite direction of $(1/12)-(25/60)\times(1/12)$ of a full rotation or $17.5^{\circ}$; the $1/12$ represents the rotation from the three o'clock hour back to the two o'clock hour, while the $(25/60)\times(1/12)$ represents the proportion that the hour hand moves as the time changes from 2:00 to 2:25.
Taken together, the angle between the two is $60^{\circ}+17.5^{\circ}$ or $77.5^{\circ}$.
A: You're so close!
As you say, the hour hand moves 30 degrees in 1 hour, hence 0.5° per minute, and therefore 12.5° from where it was at 2pm, which was at 60° from 'zero'. So at 2:25 it is at 72.5° from 'zero'.
And, like you say, the minute hand is at 150°. So just subtract 72.5° from 150°, which is 77.5° difference!
