Clock angle — What is the angle between the minute hand and the hour hand at exactly 2:18 AM?

Introduction / Context:
Compute the smaller angle between hands at a specific time using angle formulas.

Given Data / Assumptions:

• At 2:18, h = 2, m = 18.
• Hour angle = 30h + 0.5m; minute angle = 6m.

Concept / Approach:
Use angle difference = |(30h + 0.5m) − 6m|.

Step-by-Step Solution:
Hour angle = 30*2 + 0.5*18 = 60 + 9 = 69.Minute angle = 6*18 = 108.Difference = |69 − 108| = 39 degrees.

Verification / Alternative check:
The reflex angle would be 360 − 39 = 321, so the standard (smaller) angle is 39 degrees.

Why Other Options Are Wrong:
37° and 33° arise from arithmetic slips; “None” is wrong because 39° is exact.

Common Pitfalls:
Neglecting the hour-hand movement during the 18 minutes.

Final Answer:
39°.