Question

reflex angle between the hands of a clock10:25 is:

Answer 1

Answer :
we know " A Reflex Angle is more than 180$°$ but less than 360$°$ .
And
We know angle traced by hour hand in 12 hours = 360$°$

So ,
Angle traced by hour hand in 1 hour = $\frac{360°}{12}$
Therefore
Angle traced by hour hand in (10 + $\frac{25}{60}$ )hour = $\frac{360°}{12}$ $\times \left(10+\frac{25}{60}\right)$ = $\frac{360}{12}\times \left(\frac{125}{12}\right)={\left(\frac{625}{2}\right)}^{°}$

And

We know angle traced by Minute hand in 60 minutes = 360$°$

So ,
Angle traced by Minute hand in 1 minute = $\frac{360°}{60}$
Therefore
Angle traced by Minute hand in 25 minutes = ${\left(\frac{360}{60}\times 25\right)}^{°}$ = 150$°$

So,

Reflex angle between the hands of a clock at 10 : 25 = 360$°$ - ( ${\left(\frac{625}{2}\right)}^{°}$ - 150$°$ )

= 360$°$ - ${\left(\frac{625-300}{2}\right)}^{°}$

= 360$°$ - ${\left(\frac{325}{2}\right)}^{°}$

= ${\left(\frac{720-325}{2}\right)}^{°}$

= ${\left(\frac{395}{2}\right)}^{°}={\left(197\frac{1}{2}\right)}^{°}$ ( Ans )