Clock – Angle at half past four: Find the angle between the two hands of a clock at 4:30.

Introduction / Context:
Angle between clock hands at a given time is a staple aptitude task.

Given Data / Assumptions:
Time = 4:30.

Concept / Approach:
Hour hand: 30° per hour + 0.5° per minute → at 4:30, it is 4*30 + 30*0.5 = 120 + 15 = 135°. Minute hand: 30 minutes × 6° = 180°.

Step-by-Step Solution:
Angle = |180 − 135| = 45°.

Verification / Alternative check:
General formula: |30h − 5.5m| → |120 − 165| = 45.

Why Other Options Are Wrong:
30°, 40° → incorrect differences; “None” not needed.

Common Pitfalls:
Forgetting the hour hand moves during the half hour.

Final Answer:
45°