90° Clockwise

$\frac{|60h-11m|}{2} =Angle$ Since the given angle is 90 degree substituting that and o for the hour since 12 hrs is 0 we get $\frac{|60(0)-11(min)|}{2}=90$ We get $180=-11min$ dividing by -11 we get -16.36 but we cannot have negative min so the answer is simply $16.3636$ minutes. I don not know if this is possible solution.

For every $60$ divisions the minute hand moves, the hour hand moves $5$ divisons.

So for every $12$ divisions the minute hand moves, the hour hand moves $1$ division.

If $x = hours$ , $y = minutes$ , then

$12x = y$

$\implies x = \frac{y}{12}$

For the hands to create a $90°$ , there must be $15$ divisions between them.

$\implies y - x = 15$

$\implies y - \frac{y}{12} = 15$

$\implies \frac{11 y}{12} = 15$

$\implies y = \frac{180}{11} = \boxed{16.363} minutes$

Starting at 12, each minute the hour hand moves $0.5$ degrees while the minute hand moves $360 \div 60 = 6$ degrees. So each minute the minute and hour hand separates by $5.5$ degrees. So the number of minutes to be 90 degrees apart is $90 \div 5.5 = \boxed{16.3636...}$ minutes.

Let x be the angle.

As the Minutes Hand moves 6 degree (360/60) in a minute and the Hours Hand moves 0.5 Degree(360/(60*12), so the Equation will be

x 6-x .5=90

x(6-.5)=90

x=90/5.5

boxed $x=16.363636$

Basically, in a 12 hour clock, there are 360 degrees. Thus every hour, the hour hand moves $360÷12=30$ degrees. Every minute it moves 0.5 degrees. Every minute the minute hand moves $360÷60=6$ degrees. Thus $90÷(6-0.5)$ equals 16.36 degrees.