suppose that now it is $1:50$, we need to calculate angle between these hands first because we have $12$ hour system per day and night and they are equal, each hour corresponds $360/12=30$, from $10$ to $1$ we have $30+30+30=90$, but i want to know what should be degree of angle at the same time from $1$ to $2$?
Because there is $30$ degree and $5$ dot, each one should equal to $30/5=6$ right? or? please help me
On
As the Minute hand traverses, in $60$ minutes $360^\circ$
In $1$ Hour $50$ Minutes $=110$ minutes it will traverse $\frac{110}{60}\cdot 360^\circ=660^\circ\equiv300^\circ\pmod{360^\circ}$
As the Hour hand traverses, in $12$ hours $=720$ minutes $360^\circ$
In $1$ Hour $50$ Minutes $=110$ minutes it will traverse $\frac{110}{720}\cdot360^\circ=55^\circ$
So, angle at $1:50$ should be $(300-55)^\circ=245^\circ$ which is the reflex angle
So, the obtuse angle will be $|245-360|^\circ=115^\circ$
That extra angle is due to extra $50$ min. after $1:00$. For $60$ min. hour hand moves $30^\circ$, so for $50$ min. it moves by $\frac{50}{60}\cdot30^\circ=25^\circ$
So total angle b/w hr hand and min. hand at $1:50$ $=90^\circ+25^\circ=115^\circ$