At quarter past 3, the minute hand is at the 3 (15 minutes), which is at 6×15=90 degrees from the 12 o'clock position.
The hour hand at 3:15 is 30×3+6015×30=90+7.5=97.5 degrees from the 12 o'clock position.
The angle between the hour and minute hands is ∣97.5−90∣=7.5 degrees.