The angle formed by the hour-hand and the minute-hand of a clock at 2 : 15 p.m. is

Angle traced by hour hand in an hour = 30°

$herefore$ Angle traced in $2 frac{1}{4}$

i.e. $frac{9}{4}$ hours

$=frac{9}{4} imes 30^{circ}=frac{135^{circ}}{2}$

Angle traced by minute hand in 60 minutes = 360°

∴ Angle traced in 15 minutes

$=frac{360}{60} imes 15=90^{circ}$

$herefore quad$ Required angle $=90^{circ}-frac{135^{circ}}{2}$

$=frac{45}{2}=22 frac{1}{2}^{circ}$