Question

Find the measure of the smaller angle formed by hands of a clock at the following time.

$5:15$

Answer 1

Finding the the angle formed by hour hand at $5:15$:

We know that in $12-$hours the hour hand complete one revolution that is ${360}^{\circ }$.
In $1-$hour the angle formed $=\frac{{360}^{\circ }}{12}$
$={30}^{\circ }$
So, $5:15=5\frac{1}{4}\mathrm{hr}$
Angle formed by hour hand at $5:15=5\frac{1}{4}\times {30}^{\circ }$
$=157.5^{\circ }$
Angle formed by minute hand for $15$ min $=\frac{1}{4}\times {360}^{\circ }$
$={90}^{\circ }$
Angle between both hands $=157.5^{\circ }-{90}^{\circ }$
$=67.5^{\circ }$

Hence, the answer is $67.5^{\circ }$.