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'?

$7\frac{1}{2}°$

The correct answer is Option (3) → $7\frac{1}{2}°$

At quarter past the hour, the minute-hand is exactly at 3:00 but the hour-hand has moved 1/4 of the way between 3:00 and 4:00. Therefore 1/4 times 1/12 = 1/48 of the clock. With the clock having 360 degrees, 360/48 = 7.5 degrees or $7\frac{1}{2}°$