At what iem between 8 and 9 o'clock will the minute hand and the hour hand ?
make an angle of `60^(@)` with each other

Explanation

From the formula, `theta=11/2m-30h`
`" "["when "11/2m gt 30h]`
According to the question,
Here, `theta-60^(@), h=8`
So, `60-11/2m-30 times 8`
or, `m=(120+480)/11=54""6/11` minutes past 8 o.clock

Also, `theta=30h-11/2m" "["when "30h gt11/2m]`
So, `60=30 times 8-11/2m`

or, `m=(480-120)/11-360/11=32""8/11` minutes past 8 o.clock.
So, the angle between the two hands is `60^(@)` when the clock shows = 8 hours `54""6/11` and 8 hours `32""8/11` minutes.