Answer:
Option B is correct.
67.5 degree
Step-by-step explanation:
To find the angle between the hands of a clock.
Given that:
Hands of a clock at 5 : 15.
We know that:
A clock is a circle and it always contains 360 degree.
Since, there are 60 minutes on a clock.
![\frac{360^{\circ}}{60 minutes} = 6^{\circ} per minutes](https://tex.z-dn.net/?f=%5Cfrac%7B360%5E%7B%5Ccirc%7D%7D%7B60%20minutes%7D%20%3D%206%5E%7B%5Ccirc%7D%20per%20minutes)
so, each minute is 6 degree.
The minutes hand on the clock will point at 15 minute,
then, its position on the clock is:
![(15) \cdot 6^{\circ} = 90^{\circ}](https://tex.z-dn.net/?f=%2815%29%20%5Ccdot%206%5E%7B%5Ccirc%7D%20%3D%2090%5E%7B%5Ccirc%7D)
Also, there are 12 hours on the clock
⇒Each hour is 30 degree.
Now, can calculate where the hour hand at 5:00 clock.
⇒![5 \cdot 30 =150^{\circ}](https://tex.z-dn.net/?f=5%20%5Ccdot%2030%20%3D150%5E%7B%5Ccirc%7D)
Since, the hours hand is between 5 and 6 and we are looking for 5:15 then :
15 minutes is equal to
of an hour
⇒![150+\frac{1}{4}(30) = 150+7.5 = 157.5^{\circ}](https://tex.z-dn.net/?f=150%2B%5Cfrac%7B1%7D%7B4%7D%2830%29%20%3D%20150%2B7.5%20%3D%20157.5%5E%7B%5Ccirc%7D)
Then the angle between two hands of clock:
⇒![\theta = 150.75 -90 = 67.5^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20150.75%20-90%20%3D%2067.5%5E%7B%5Ccirc%7D)
Therefore, the angle between the hands of a clock at 5: 15 is: 67.5 degree.