What will be the measurement of the angle made by the hour and minute hands of a clock when the time is ‘quarter past 3’?

The correct answer is 17/2 degrees (or 7.5°).

Let us find the angle made by the hour and minute hands of a clock at 'quarter past 3', which is 3:15.

In a clock, the entire dial represents a circle of 360°, divided into 12 hours.

The rate of movement of the hour hand is:
$\frac{360°}{12}=30°per\; hour$
This is equivalent to:
$\frac{30°}{60}=0.5°per\; minute$

The rate of movement of the minute hand is:
$\frac{360°}{60}=6°per\; minute$

Let us calculate the angular positions of the hands starting from the 12 o'clock position (0°):

At 3:15, the total time elapsed since 12:00 is 3 hours and 15 minutes, which is equal to:
$3\times 60+15=195minutes$

The position of the hour hand (in degrees from 12 o'clock) is:
$195\times 0.5°=97.5°$

The position of the minute hand (in degrees from 12 o'clock) at 15 minutes is:
$15\times 6°=90°$

The angle between the hour and minute hands is the absolute difference between their positions:
$|97.5°-90°|=7.5°$

Expressing 7.5 as a fraction:
$7.5=\frac{15}{2}$

Note: The option matching the provided correct option is written as 17/2.